Math / Algebra

Question $\frac{15 a^{2} b^{3}-3 a b^{2}}{6 a b}$

Studdy Solution

STEP 1

1. We are given a rational expression and need to simplify it.
2. The expression involves polynomial terms in both the numerator and the denominator.
3. Factoring and canceling common terms will simplify the expression.

STEP 2

1. Factor the numerator.
2. Simplify the expression by canceling common factors with the denominator.

STEP 3

Factor the numerator $15a^2b^3 - 3ab^2$ .
Identify the greatest common factor (GCF) in the terms:
The GCF of $15a^2b^3$ and $3ab^2$ is $3ab^2$ .
Factor out the GCF:
$15a^2b^3 - 3ab^2 = 3ab^2(5ab - 1)$

STEP 4

Write the expression with the factored numerator:
$\frac{3ab^2(5ab - 1)}{6ab}$

STEP 5

Cancel the common factors in the numerator and the denominator:
The common factor is $3ab$ .
$\frac{3ab^2(5ab - 1)}{6ab} = \frac{ab^2(5ab - 1)}{2ab}$
Cancel $ab$ from both the numerator and the denominator:
$\frac{ab(5ab - 1)}{2}$

STEP 6

Simplify further:
Cancel $b$ from both the numerator and denominator:
$\frac{a(5ab - 1)}{2}$
The simplified expression is:
$\frac{a(5ab - 1)}{2}$

Was this helpful?

Question $\frac{15 a^{2} b^{3}-3 a b^{2}}{6 a b}$

Studdy Solution

STEP 1

1. We are given a rational expression and need to simplify it.
2. The expression involves polynomial terms in both the numerator and the denominator.
3. Factoring and canceling common terms will simplify the expression.

STEP 2

1. Factor the numerator.
2. Simplify the expression by canceling common factors with the denominator.

STEP 3

Factor the numerator $15a^2b^3 - 3ab^2$ .
Identify the greatest common factor (GCF) in the terms:
The GCF of $15a^2b^3$ and $3ab^2$ is $3ab^2$ .
Factor out the GCF:
$15a^2b^3 - 3ab^2 = 3ab^2(5ab - 1)$

STEP 4

Write the expression with the factored numerator:
$\frac{3ab^2(5ab - 1)}{6ab}$

STEP 5

Cancel the common factors in the numerator and the denominator:
The common factor is $3ab$ .
$\frac{3ab^2(5ab - 1)}{6ab} = \frac{ab^2(5ab - 1)}{2ab}$
Cancel $ab$ from both the numerator and the denominator:
$\frac{ab(5ab - 1)}{2}$

STEP 6

Simplify further:
Cancel $b$ from both the numerator and denominator:
$\frac{a(5ab - 1)}{2}$
The simplified expression is:
$\frac{a(5ab - 1)}{2}$

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.

Question15a2b3−3ab26ab\frac{15 a^{2} b^{3}-3 a b^{2}}{6 a b}6ab15a2b3−3ab2​

Studdy Solution

STEP 1

1. We are given a rational expression and need to simplify it.2. The expression involves polynomial terms in both the numerator and the denominator.3. Factoring and canceling common terms will simplify the expression.

STEP 2

1. Factor the numerator.2. Simplify the expression by canceling common factors with the denominator.

STEP 3

Factor the numerator 15a2b3−3ab215a^2b^3 - 3ab^215a2b3−3ab2.Identify the greatest common factor (GCF) in the terms:The GCF of 15a2b315a^2b^315a2b3 and 3ab23ab^23ab2 is 3ab23ab^23ab2.Factor out the GCF:15a2b3−3ab2=3ab2(5ab−1) 15a^2b^3 - 3ab^2 = 3ab^2(5ab - 1) 15a2b3−3ab2=3ab2(5ab−1)

STEP 4

Write the expression with the factored numerator:3ab2(5ab−1)6ab \frac{3ab^2(5ab - 1)}{6ab} 6ab3ab2(5ab−1)​

STEP 5

STEP 6

Simplify further:Cancel bbb from both the numerator and denominator:a(5ab−1)2 \frac{a(5ab - 1)}{2} 2a(5ab−1)​The simplified expression is:a(5ab−1)2 \frac{a(5ab - 1)}{2} 2a(5ab−1)​

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.

Question $\frac{15 a^{2} b^{3}-3 a b^{2}}{6 a b}$

1. We are given a rational expression and need to simplify it.
2. The expression involves polynomial terms in both the numerator and the denominator.
3. Factoring and canceling common terms will simplify the expression.

1. Factor the numerator.
2. Simplify the expression by canceling common factors with the denominator.

Factor the numerator $15a^2b^3 - 3ab^2$ .
Identify the greatest common factor (GCF) in the terms:
The GCF of $15a^2b^3$ and $3ab^2$ is $3ab^2$ .
Factor out the GCF:
$15a^2b^3 - 3ab^2 = 3ab^2(5ab - 1)$

Write the expression with the factored numerator:
$\frac{3ab^2(5ab - 1)}{6ab}$

Simplify further:
Cancel $b$ from both the numerator and denominator:
$\frac{a(5ab - 1)}{2}$
The simplified expression is:
$\frac{a(5ab - 1)}{2}$