Simplify

Problem 3301

1. Скоротіть дріб: $\frac{5 x y}{25 x^{2} y}$ a) $5 x y$ б) $\frac{1}{5 x}$ в) $\frac{1}{x}$ г) Свій варіант

See Solution

Problem 3302

Simplify. $\frac{4}{x-1}-\frac{x+5}{x+1}$

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Problem 3303

5. Differentiate and simplify: (a) $f(x):=\frac{x}{1+x^{2}}$ , (b) $g(x):=\sqrt{5-2 x+x^{2}}$ , (c) $h(x):=\left(\sin x^{k}\right)^{m}$ for $m, k \in \mathbb{N}$ , (d) $k(x):=\tan \left(x^{2}\right)$ for $|x|<\sqrt{\pi / 2}$ .

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Problem 3304

The functions $f$ and $g$ are defined $f(x)=x^{2}-x-4 \quad \text { and } \quad g(x)=\frac{x-3}{9 x-5}$
Find $f(x+8)$ and $g\left(\frac{x}{4}\right)$ . Write your answers without pare possible. $\begin{array}{l} f(x+8)= \\ g\left(\frac{x}{4}\right)=\square \end{array}$

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Problem 3305

$\log 0.36$

See Solution

Problem 3306

Factor. $s^{2}+8 s d+15 d^{2}$

See Solution

Problem 3307

Factor by grouping. $x^{3}+9 x^{2}+9 x+81$

See Solution

Problem 3308

Factor completely. $b^{5}-4 b^{4}+4 b^{3}$

See Solution

Problem 3309

Factor completely. $16 a^{2}-81$

See Solution

Problem 3310

Factor completely. $9-s^{2}$

See Solution

Problem 3311

For the function $f(x)=5 x-1$ , find each of the following. (a) $f(p)$ $f(p)=5 p-1$ (Simplify your answer.) (b) $f(-r)$ $f(-r)=-5 r-1$ (Simplify your answer.) (c) $f(m-2)$ $f(m-2)=$ $\square$ (Simplify your answer.)

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Problem 3312

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece $\sin 165^{\circ}-\sin 75^{\circ}=$ $\square$ $\sqrt{\text { 延 }}$

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Problem 3313

Difference of S Ex: Factor $x^{2}-16=x^{2}+0 x-16$

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Problem 3314

Simplify. $\left(v^{-6}\right)^{-6}$
Write your answer without using negative exponents.

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Problem 3315

Factor by grouping. $6 x^{3}-12 x^{2}-7 x+14$

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Problem 3316

Simplify. $\sqrt{v^{14}}$
Assume that the variable represents a positive real number.

See Solution

Problem 3317

Factor. $128 c^{2}-50$

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Problem 3318

$-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}$

See Solution

Problem 3319

Write an equivalent expression $-6)^{4}(y-4) 1$
Select all that apply A. $-6(4 y-4)$ B $-6\left(x_{y}-16\right)$ C. $-24 y+96$ D. $-6 y=$ vel E. $-24 y-96$

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Problem 3320

Rewrite the following without an exponent. $(-3)^{-2}$

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Problem 3321

isentity whichic expressions are equivalent to the given expression $2(2 y+2)$
Which of the following is equivalent to the expression $2(2 y+2)$ ? Select all that apply. A. $4 y+6$ - 2 - $+2=2$ y C. $4 y+4$

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Problem 3322

$\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}$

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Problem 3323

[EX1] Simplify each rational expres (1) $\frac{5 x}{6}+\frac{3-x}{4}$

See Solution

Problem 3324

Calculate the result of the complex division: $(-38+135 i) \div(11-10 i)$ .

See Solution

Problem 3325

Simplify $\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}$ and express it as $a + bi$ .

See Solution

Problem 3326

Factor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

See Solution

Problem 3327

Solve the equation $-2x^2 - 20x - 42 = 0$ by first dividing by $-2$ .

See Solution

Problem 3328

Convert the hyperbola equation $16x^{2}-9y^{2}+32x-18y-137=0$ to standard form and graph it.

See Solution

Problem 3329

Divide 72 by 5, then divide that result by 7. What is the final answer?

See Solution

Problem 3330

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ .

See Solution

Problem 3331

Calculate $29 \cdot 40 \div 12$ .

See Solution

Problem 3332

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ . Also, simplify: $2.9 \times 10^{5}$ , $56 \times 10^{-4}$ .

See Solution

Problem 3333

Calculate $(187-88)+1-(130-31)$ .

See Solution

Problem 3334

Simplify $4^{7}, 8^{5}, 2^{16}, 64^{3}$ and the expressions in problems 44 and 45 with positive indices.

See Solution

Problem 3335

Express $\left(\frac{1}{125}\right)^{600}$ as $5^{n}$ for some integer $n$ .

See Solution

Problem 3336

Express $4^{x+1}+12(4^{x})$ as a power of $4$ . Then simplify $\frac{(4^{3 x})(5^{6 x})}{10^{4 x}}$ as a power of $10$ .

See Solution

Problem 3337

Simplify $2(3^{n+2}) - 2(3^{n})$ and then $\frac{2(3^{n+2}) - 2(3^{n})}{6 \times 3^{n-1}}$ .

See Solution

Problem 3338

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

See Solution

Problem 3339

Calculate the difference quotient for $f(x)=x^{2}+5$ : find $\frac{f(x+h)-f(x)}{h}$ and simplify, where $h \neq 0$ .

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Problem 3340

Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=4x$ , where $h \neq 0$ .

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Problem 3341

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , with $h \neq 0$ . Simplify your answer.

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Problem 3342

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{10}{x^{2}}$ , where $h \neq 0$ . Simplify your answer.

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Problem 3343

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{11}{x^{2}}$ , simplifying your answer.

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Problem 3344

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{5 x}{x+6}$ , where $h \neq 0$ . Simplify your answer.

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Problem 3345

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , $h \neq 0$ . Simplify your answer.

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Problem 3346

Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{2}{x}$ , where $h \neq 0$ .

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Problem 3347

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{9}{x^{2}}$ , simplifying where $h \neq 0$ .

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Problem 3348

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-5 x+9$ , where $h \neq 0$ . Simplify your answer.

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Problem 3349

Calculate the product: $P = \frac{-3}{5} \cdot \frac{2}{-7} \cdot \frac{-5}{8} \cdot \frac{3}{-10}$ .

See Solution

Problem 3350

Calculate $(-13)+(-7)[(-2)(-3)]-[(-7)(-3)](-2)$ .

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Problem 3351

Calculate $6 \cdot(-7)\cdot[(-2)\cdot(-3)]-[-(-7)\cdot(-3)]\cdot(-2)$ .

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Problem 3352

Simplify the expression: $(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})$ .

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Problem 3353

Calculate the value of $2.75+\sqrt{2}-\sqrt{2}+75$ .

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Problem 3354

Calculate: $5 \cdot(-13) + 45 - (-45) + 13$

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Problem 3355

Solve $x^{2}+4 x=-1$ . Hint: Add 4 to both sides to form a perfect square.

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Problem 3356

Simplify the expression and ensure all exponents are positive:
$\frac{(-5)^{3} x^{3}(y z)^{4}}{(2)^{3} x y^{8} z}$

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Problem 3357

Multiply the polynomial $(-3 x^{2}-5)$ by the monomial $-3 x$ using the distributive property.

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Problem 3358

Simplify the expression: $\frac{(-5)^{3} x^{7}(y z)^{3}}{(4)^{2} x^{5} y^{7} z^{2}}$

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Problem 3359

Multiply the binomials using FOIL and combine like terms: $(x-1)(x+3)$ .

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Problem 3360

Multiply and simplify: $3x(2x+5) + 2(2x+5)$ .

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Problem 3361

Multiply the polynomials and combine like terms: $(-x+1)(5 x^{2}-4 x-8)$

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Problem 3362

Simplify the expression $\frac{x^{4} y^{4}}{x^{2} y^{5}}$ assuming bases are not 0 for 0 or negative exponents.

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Problem 3363

Multiply the polynomials $(x-1)(8x+9)$ using the distributive property and combine like terms.

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Problem 3364

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches. Simplify your expression.

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Problem 3365

Multiply and simplify: $3 x^{2}(9 x^{5}-4 x^{2}+5)$

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Problem 3366

Multiply the polynomials and combine like terms: $(x+4)(x+3)$ .

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Problem 3367

Simplify the expression $\left(x^{8} y^{-4}\right)^{3}$ .

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Problem 3368

Simplify the expression $\left(x^{9} y^{-8}\right)^{3}$ .

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Problem 3369

Simplify the expression: $\left(3 g^{6}\right)^{3}$ .

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Problem 3370

Multiply the polynomials and combine like terms: $(7x - 5)(x + 2)$ .

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Problem 3371

Simplify the expression: $(2^{-2})^{-3}$ .

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Problem 3372

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches.

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Problem 3373

Multiply the binomials using FOIL and combine like terms: $(x+9)(x-8)$ .

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Problem 3374

Multiply and simplify: $-5 x^{2}(9 x^{3}+6 x^{2}-5)$

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Problem 3375

Multiply and simplify: $4 x^{2}(9 x^{4}-5 x^{3}+4)$ .

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Problem 3376

Multiply and simplify: $5x(5x+2) + 4(5x+2)$ .

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Problem 3377

Multiply and simplify: $-2 x^{6}(5 x^{6}+3 x^{3}+7)$

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Problem 3378

Multiply the polynomials $(x+7)(x+1)$ using the distributive property and combine like terms.

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Problem 3379

Simplify the expression: $7s - 3s$ .

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Problem 3380

Simplify the expression by combining like terms: $-3x + 9x$ .

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Problem 3381

Find the simplest interval form for the intersection of the sets $(-\infty,-2]$ and $[-10, \infty)$ .

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Problem 3382

Evaluate $(x+y)^{2}-9z$ at $x=4, y=-4, z=-4$ and simplify.

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Problem 3383

Evaluate and simplify the expression $-3(y-5)-2(y+1)$ for $y=2$ .

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Problem 3384

Simplify $\left(\frac{3 a}{b^{-3}}\right)^{3}$ using only positive exponents.

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Problem 3385

Simplify the expression with positive exponents: $s^{8} \cdot s^{5}$ .

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Problem 3386

Simplify the expression: $-4^{2}$ .

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Problem 3387

Simplify the expression $\frac{x^{-6}}{x}$ using only positive exponents.

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Problem 3388

Simplify the expression with positive exponents: $\left(\frac{-2 a^{3}}{b^{-3}}\right)^{2}$ .

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Problem 3389

Simplify the expression with positive exponents: $\left(\frac{-3 a^{2}}{b^{-1}}\right)^{3}$ .

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Problem 3390

Simplify the expression with positive exponents: $\frac{z^{9}}{z^{3}}$ .

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Problem 3391

Simplify the expression using positive exponents: $\frac{5 z^{-7}}{(y^{-5})^{-3}}$ .

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Problem 3392

Simplify the expression using positive exponents: $\frac{-4 y^{5}}{\left(z^{-3}\right)^{-5}}$ .

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Problem 3393

Convert -0.000354 to scientific notation.

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Problem 3394

Simplify the expression with positive exponents: $n^{8} \cdot n^{4}$ .

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Problem 3395

Simplify the expression: $-4^{2}$ .

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Problem 3396

Simplify the expression using positive exponents: $-\frac{3 y}{(x^{3})^{-2}}$ .

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Problem 3397

Simplify the expression using positive exponents: $\frac{5 x^{11}}{(y^{2})^{7}}$ .

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Problem 3398

Simplify the expression with positive exponents: $\frac{z^{-1}}{z^{-3}}$ .

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Problem 3399

Multiply. Write your answer in simplest form. $\sqrt{35} \cdot 9 \sqrt{30}$ $\square$ Submit

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Problem 3400

Multiply. Write your answer in simplest form. $\sqrt{242} \cdot \sqrt{11}$ $\square$ Submit

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1 ...31 32 33 34 35 36 37 ...56

Simplify

Problem 3301

1. Скоротіть дріб: 5xy25x2y\frac{5 x y}{25 x^{2} y}25x2y5xy​ a) 5xy5 x y5xy б) 15x\frac{1}{5 x}5x1​ в) 1x\frac{1}{x}x1​ г) Свій варіант

Problem 3302

Simplify. 4x−1−x+5x+1\frac{4}{x-1}-\frac{x+5}{x+1}x−14​−x+1x+5​

Problem 3303

Problem 3304

Problem 3305

log⁡0.36\log 0.36log0.36

Problem 3306

Factor. s2+8sd+15d2s^{2}+8 s d+15 d^{2}s2+8sd+15d2

Problem 3307

Factor by grouping. x3+9x2+9x+81x^{3}+9 x^{2}+9 x+81x3+9x2+9x+81

Problem 3308

Factor completely. b5−4b4+4b3b^{5}-4 b^{4}+4 b^{3}b5−4b4+4b3

Problem 3309

Factor completely. 16a2−8116 a^{2}-8116a2−81

Problem 3310

Factor completely. 9−s29-s^{2}9−s2

Problem 3311

Problem 3312

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece sin⁡165∘−sin⁡75∘=\sin 165^{\circ}-\sin 75^{\circ}=sin165∘−sin75∘= □\square□ 延 \sqrt{\text { 延 }} 延 ​

Problem 3313

Difference of S Ex: Factor x2−16=x2+0x−16x^{2}-16=x^{2}+0 x-16x2−16=x2+0x−16

Problem 3314

Simplify. (v−6)−6\left(v^{-6}\right)^{-6}(v−6)−6Write your answer without using negative exponents.

Problem 3315

Factor by grouping. 6x3−12x2−7x+146 x^{3}-12 x^{2}-7 x+146x3−12x2−7x+14

Problem 3316

Simplify. v14\sqrt{v^{14}}v14​Assume that the variable represents a positive real number.

Problem 3317

Factor. 128c2−50128 c^{2}-50128c2−50

Problem 3318

−(−82)2+1−(−3)2-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}−(2−8​)2+1−(−3)2

Problem 3319

Write an equivalent expression −6)4(y−4)1-6)^{4}(y-4) 1−6)4(y−4)1Select all that apply A. −6(4y−4)-6(4 y-4)−6(4y−4) B −6(xy−16)-6\left(x_{y}-16\right)−6(xy​−16) C. −24y+96-24 y+96−24y+96 D. −6y=-6 y=−6y= vel E. −24y−96-24 y-96−24y−96

Problem 3320

Rewrite the following without an exponent. (−3)−2(-3)^{-2}(−3)−2

Problem 3321

isentity whichic expressions are equivalent to the given expression 2(2y+2)2(2 y+2)2(2y+2)Which of the following is equivalent to the expression 2(2y+2)2(2 y+2)2(2y+2) ? Select all that apply. A. 4y+64 y+64y+6 - 2 - +2=2+2=2+2=2 y C. 4y+44 y+44y+4

Problem 3322

−(8)2=−(−6)3=\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}−(8)2=−(−6)3=​

Problem 3323

[EX1] Simplify each rational expres (1) 5x6+3−x4\frac{5 x}{6}+\frac{3-x}{4}65x​+43−x​

Problem 3324

Calculate the result of the complex division: (−38+135i)÷(11−10i)(-38+135 i) \div(11-10 i)(−38+135i)÷(11−10i).

Problem 3325

Simplify −1−9−7\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}−9​−7​−1​​ and express it as a+bia + bia+bi.

Problem 3326

Factor the GCF from the polynomial: 25x6+5x4+35x325 x^{6}+5 x^{4}+35 x^{3}25x6+5x4+35x3.

Problem 3327

Solve the equation −2x2−20x−42=0-2x^2 - 20x - 42 = 0−2x2−20x−42=0 by first dividing by −2-2−2.

Problem 3328

Convert the hyperbola equation 16x2−9y2+32x−18y−137=016x^{2}-9y^{2}+32x-18y-137=016x2−9y2+32x−18y−137=0 to standard form and graph it.

Problem 3329

Divide 72 by 5, then divide that result by 7. What is the final answer?

Problem 3330

Convert these numbers to scientific notation: 0.00000056, -193.47, 0.0531×1080.0531 \times 10^{8}0.0531×108, −3671×105-3671 \times 10^{5}−3671×105.

Problem 3331

Calculate 29⋅40÷1229 \cdot 40 \div 1229⋅40÷12.

Problem 3332

Convert these numbers to scientific notation: 0.00000056, -193.47, 0.0531×1080.0531 \times 10^{8}0.0531×108, −3671×105-3671 \times 10^{5}−3671×105. Also, simplify: 2.9×1052.9 \times 10^{5}2.9×105, 56×10−456 \times 10^{-4}56×10−4.

Problem 3333

Calculate (187−88)+1−(130−31)(187-88)+1-(130-31)(187−88)+1−(130−31).

Problem 3334

Simplify 47,85,216,6434^{7}, 8^{5}, 2^{16}, 64^{3}47,85,216,643 and the expressions in problems 44 and 45 with positive indices.

Problem 3335

Express (1125)600\left(\frac{1}{125}\right)^{600}(1251​)600 as 5n5^{n}5n for some integer nnn.

Problem 3336

Express 4x+1+12(4x)4^{x+1}+12(4^{x})4x+1+12(4x) as a power of 444. Then simplify (43x)(56x)104x\frac{(4^{3 x})(5^{6 x})}{10^{4 x}}104x(43x)(56x)​ as a power of 101010.

Problem 3337

Simplify 2(3n+2)−2(3n)2(3^{n+2}) - 2(3^{n})2(3n+2)−2(3n) and then 2(3n+2)−2(3n)6×3n−1\frac{2(3^{n+2}) - 2(3^{n})}{6 \times 3^{n-1}}6×3n−12(3n+2)−2(3n)​.

Problem 3338

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=7x+7f(x)=7x+7f(x)=7x+7, where h≠0h \neq 0h=0. Simplify your answer.

Problem 3339

Calculate the difference quotient for f(x)=x2+5f(x)=x^{2}+5f(x)=x2+5: find f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ and simplify, where h≠0h \neq 0h=0.

Problem 3340

Find and simplify the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=4xf(x)=4xf(x)=4x, where h≠0h \neq 0h=0.

Problem 3341

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for f(x)=3xx+3f(x)=\frac{3x}{x+3}f(x)=x+33x​, with h≠0h \neq 0h=0. Simplify your answer.

1. Скоротіть дріб: $\frac{5 x y}{25 x^{2} y}$ a) $5 x y$ б) $\frac{1}{5 x}$ в) $\frac{1}{x}$ г) Свій варіант

Simplify. $\frac{4}{x-1}-\frac{x+5}{x+1}$

$\log 0.36$

Factor. $s^{2}+8 s d+15 d^{2}$

Factor by grouping. $x^{3}+9 x^{2}+9 x+81$

Factor completely. $b^{5}-4 b^{4}+4 b^{3}$

Factor completely. $16 a^{2}-81$

Factor completely. $9-s^{2}$

Use a sum-to-product formula to find the exact value. Write your answer as a simplified fraction and rationalize the denominator, if nece $\sin 165^{\circ}-\sin 75^{\circ}=$ $\square$ $\sqrt{\text { 延 }}$

Difference of S Ex: Factor $x^{2}-16=x^{2}+0 x-16$

Simplify. $\left(v^{-6}\right)^{-6}$
Write your answer without using negative exponents.

Factor by grouping. $6 x^{3}-12 x^{2}-7 x+14$

Simplify. $\sqrt{v^{14}}$
Assume that the variable represents a positive real number.

Factor. $128 c^{2}-50$

$-\left(\frac{-8}{2}\right)^{2}+1-(-3)^{2}$

Write an equivalent expression $-6)^{4}(y-4) 1$
Select all that apply A. $-6(4 y-4)$ B $-6\left(x_{y}-16\right)$ C. $-24 y+96$ D. $-6 y=$ vel E. $-24 y-96$

Rewrite the following without an exponent. $(-3)^{-2}$

isentity whichic expressions are equivalent to the given expression $2(2 y+2)$
Which of the following is equivalent to the expression $2(2 y+2)$ ? Select all that apply. A. $4 y+6$ - 2 - $+2=2$ y C. $4 y+4$

$\begin{array}{c}-(8)^{2}= \\ -(-6)^{3}=\end{array}$

[EX1] Simplify each rational expres (1) $\frac{5 x}{6}+\frac{3-x}{4}$

Calculate the result of the complex division: $(-38+135 i) \div(11-10 i)$ .

Simplify $\frac{\sqrt{-1}}{\sqrt{-9} \sqrt{-7}}$ and express it as $a + bi$ .

Factor the GCF from the polynomial: $25 x^{6}+5 x^{4}+35 x^{3}$ .

Solve the equation $-2x^2 - 20x - 42 = 0$ by first dividing by $-2$ .

Convert the hyperbola equation $16x^{2}-9y^{2}+32x-18y-137=0$ to standard form and graph it.

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ .

Calculate $29 \cdot 40 \div 12$ .

Convert these numbers to scientific notation: 0.00000056, -193.47, $0.0531 \times 10^{8}$ , $-3671 \times 10^{5}$ . Also, simplify: $2.9 \times 10^{5}$ , $56 \times 10^{-4}$ .

Calculate $(187-88)+1-(130-31)$ .

Simplify $4^{7}, 8^{5}, 2^{16}, 64^{3}$ and the expressions in problems 44 and 45 with positive indices.

Express $\left(\frac{1}{125}\right)^{600}$ as $5^{n}$ for some integer $n$ .

Express $4^{x+1}+12(4^{x})$ as a power of $4$ . Then simplify $\frac{(4^{3 x})(5^{6 x})}{10^{4 x}}$ as a power of $10$ .

Simplify $2(3^{n+2}) - 2(3^{n})$ and then $\frac{2(3^{n+2}) - 2(3^{n})}{6 \times 3^{n-1}}$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=7x+7$ , where $h \neq 0$ . Simplify your answer.

Calculate the difference quotient for $f(x)=x^{2}+5$ : find $\frac{f(x+h)-f(x)}{h}$ and simplify, where $h \neq 0$ .

Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=4x$ , where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , with $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{10}{x^{2}}$ , where $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{11}{x^{2}}$ , simplifying your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{5 x}{x+6}$ , where $h \neq 0$ . Simplify your answer.

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{3x}{x+3}$ , $h \neq 0$ . Simplify your answer.

Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{2}{x}$ , where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=\frac{9}{x^{2}}$ , simplifying where $h \neq 0$ .

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}-5 x+9$ , where $h \neq 0$ . Simplify your answer.

Calculate the product: $P = \frac{-3}{5} \cdot \frac{2}{-7} \cdot \frac{-5}{8} \cdot \frac{3}{-10}$ .

Calculate $(-13)+(-7)[(-2)(-3)]-[(-7)(-3)](-2)$ .

Calculate $6 \cdot(-7)\cdot[(-2)\cdot(-3)]-[-(-7)\cdot(-3)]\cdot(-2)$ .

Simplify the expression: $(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})$ .

Calculate the value of $2.75+\sqrt{2}-\sqrt{2}+75$ .

Calculate: $5 \cdot(-13) + 45 - (-45) + 13$

Solve $x^{2}+4 x=-1$ . Hint: Add 4 to both sides to form a perfect square.

Simplify the expression and ensure all exponents are positive:
$\frac{(-5)^{3} x^{3}(y z)^{4}}{(2)^{3} x y^{8} z}$

Multiply the polynomial $(-3 x^{2}-5)$ by the monomial $-3 x$ using the distributive property.

Simplify the expression: $\frac{(-5)^{3} x^{7}(y z)^{3}}{(4)^{2} x^{5} y^{7} z^{2}}$

Multiply the binomials using FOIL and combine like terms: $(x-1)(x+3)$ .

Multiply and simplify: $3x(2x+5) + 2(2x+5)$ .

Multiply the polynomials and combine like terms: $(-x+1)(5 x^{2}-4 x-8)$

Simplify the expression $\frac{x^{4} y^{4}}{x^{2} y^{5}}$ assuming bases are not 0 for 0 or negative exponents.

Multiply the polynomials $(x-1)(8x+9)$ using the distributive property and combine like terms.

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches. Simplify your expression.

Multiply and simplify: $3 x^{2}(9 x^{5}-4 x^{2}+5)$

Multiply the polynomials and combine like terms: $(x+4)(x+3)$ .

Simplify the expression $\left(x^{8} y^{-4}\right)^{3}$ .

Simplify the expression $\left(x^{9} y^{-8}\right)^{3}$ .

Simplify the expression: $\left(3 g^{6}\right)^{3}$ .

Multiply the polynomials and combine like terms: $(7x - 5)(x + 2)$ .

Simplify the expression: $(2^{-2})^{-3}$ .

Find the area of a poster with length $6x$ inches and width $5x + 6$ inches.

Multiply the binomials using FOIL and combine like terms: $(x+9)(x-8)$ .

Multiply and simplify: $-5 x^{2}(9 x^{3}+6 x^{2}-5)$