Math / Algebra

QuestionUse either method to simplify the complex fraction. $\begin{array}{l} \frac{\frac{1}{x}+17}{-\frac{1}{x}+17} \\ \frac{\frac{1}{x}+17}{-\frac{1}{x}+17}= \end{array}$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a big fraction that has little fractions inside it, which is called a complex fraction! Watch out! Don't forget to distribute when multiplying the top and bottom of the big fraction!

STEP 2

1. Find the least common denominator (LCD)
2. Multiply the top and bottom by the LCD
3. Simplify

STEP 3

The little fractions inside the big fraction have denominators of $x$ .
So, our least common denominator (LCD) is just $x$ !
This is what we'll use to simplify things.

STEP 4

We're going to multiply the top and bottom of our big fraction by our LCD, which is $x$ .
This is like multiplying by $1$ , so it doesn't change the value of the fraction, just how it looks!

STEP 5

Multiplying the top: $x \cdot \left( \frac{1}{x} + 17 \right) = x \cdot \frac{1}{x} + x \cdot 17 = \frac{x}{x} + 17x = 1 + 17x$ We distributed the $x$ to both terms inside the parentheses.
Remember, $x$ divided by $x$ is $1$ , as long as $x$ isn't zero!

STEP 6

Multiplying the bottom: $x \cdot \left( -\frac{1}{x} + 17 \right) = x \cdot \left(-\frac{1}{x}\right) + x \cdot 17 = -\frac{x}{x} + 17x = -1 + 17x$ Again, we distributed, and $x$ divided by $x$ is $1$ , so we get $-1$ since we had a negative sign.

STEP 7

Now, let's put it all together!
Our simplified fraction is: $\frac{1 + 17x}{-1 + 17x}$ Look at that, no more little fractions inside!

STEP 8

Our simplified complex fraction is $\frac{1 + 17x}{-1 + 17x}$ .

Was this helpful?

QuestionUse either method to simplify the complex fraction. $\begin{array}{l} \frac{\frac{1}{x}+17}{-\frac{1}{x}+17} \\ \frac{\frac{1}{x}+17}{-\frac{1}{x}+17}= \end{array}$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a big fraction that has little fractions inside it, which is called a complex fraction! Watch out! Don't forget to distribute when multiplying the top and bottom of the big fraction!

STEP 2

1. Find the least common denominator (LCD)
2. Multiply the top and bottom by the LCD
3. Simplify

STEP 3

The little fractions inside the big fraction have denominators of $x$ .
So, our least common denominator (LCD) is just $x$ !
This is what we'll use to simplify things.

STEP 4

We're going to multiply the top and bottom of our big fraction by our LCD, which is $x$ .
This is like multiplying by $1$ , so it doesn't change the value of the fraction, just how it looks!

STEP 5

Multiplying the top: $x \cdot \left( \frac{1}{x} + 17 \right) = x \cdot \frac{1}{x} + x \cdot 17 = \frac{x}{x} + 17x = 1 + 17x$ We distributed the $x$ to both terms inside the parentheses.
Remember, $x$ divided by $x$ is $1$ , as long as $x$ isn't zero!

STEP 6

Multiplying the bottom: $x \cdot \left( -\frac{1}{x} + 17 \right) = x \cdot \left(-\frac{1}{x}\right) + x \cdot 17 = -\frac{x}{x} + 17x = -1 + 17x$ Again, we distributed, and $x$ divided by $x$ is $1$ , so we get $-1$ since we had a negative sign.

STEP 7

Now, let's put it all together!
Our simplified fraction is: $\frac{1 + 17x}{-1 + 17x}$ Look at that, no more little fractions inside!

STEP 8

Our simplified complex fraction is $\frac{1 + 17x}{-1 + 17x}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionUse either method to simplify the complex fraction. 1x+17−1x+171x+17−1x+17=\begin{array}{l} \frac{\frac{1}{x}+17}{-\frac{1}{x}+17} \\ \frac{\frac{1}{x}+17}{-\frac{1}{x}+17}= \end{array}−x1​+17x1​+17​−x1​+17x1​+17​=​ □\square□ (Simplify your answer.)

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a big fraction that has little fractions inside it, which is called a complex fraction! Watch out! Don't forget to distribute when multiplying the top and bottom of the big fraction!

STEP 2

1. Find the least common denominator (LCD)2. Multiply the top and bottom by the LCD3. Simplify

STEP 3

The little fractions inside the big fraction have denominators of xxx.So, our **least common denominator (LCD)** is just xxx!This is what we'll use to simplify things.

STEP 4

We're going to multiply the **top** and **bottom** of our big fraction by our **LCD**, which is xxx.This is like multiplying by 111, so it doesn't change the *value* of the fraction, just how it looks!

STEP 5

STEP 6

STEP 7

Now, let's put it all together!Our simplified fraction is: 1+17x−1+17x \frac{1 + 17x}{-1 + 17x} −1+17x1+17x​ Look at that, no more little fractions inside!

STEP 8

Our simplified complex fraction is 1+17x−1+17x\frac{1 + 17x}{-1 + 17x}−1+17x1+17x​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionUse either method to simplify the complex fraction. $\begin{array}{l} \frac{\frac{1}{x}+17}{-\frac{1}{x}+17} \\ \frac{\frac{1}{x}+17}{-\frac{1}{x}+17}= \end{array}$ $\square$ (Simplify your answer.)

1. Find the least common denominator (LCD)
2. Multiply the top and bottom by the LCD
3. Simplify

The little fractions inside the big fraction have denominators of $x$ .
So, our least common denominator (LCD) is just $x$ !
This is what we'll use to simplify things.

We're going to multiply the top and bottom of our big fraction by our LCD, which is $x$ .
This is like multiplying by $1$ , so it doesn't change the value of the fraction, just how it looks!

Now, let's put it all together!
Our simplified fraction is: $\frac{1 + 17x}{-1 + 17x}$ Look at that, no more little fractions inside!

Our simplified complex fraction is $\frac{1 + 17x}{-1 + 17x}$ .