Divide. Write your answer in simplest form. (g- 1)/(10g^3 + 25g^2) ÷ (g- 1) ______

Rewrite division as multiplication: Rewrite the division as a multiplication by the reciprocal of the second expression. (g - 1)/(10g^3 + 25g^2) ÷ (g - 1) can be rewritten as (g - 1)/(10g^3 + 25g^2) × 1/(g - 1).Factor out GCF from denominator: Factor out the greatest common factor (GCF) from the denominator of the first fraction. The GCF of 10g^3 and 25g^2 is 5g^2, so factor that out to get (g - 1)/(5g^2(2g + 5)).Multiply numerators and denominators: Multiply the numerators and the denominators of the two fractions. (g - 1)/(5g^2(2g + 5)) × 1/(g - 1) = (g - 1) * 1 / (5g^2(2g + 5) * (g - 1)).Cancel out terms: Cancel out the (g - 1) terms in the numerator and the denominator. After canceling, the expression simplifies to 1 / (5g^2(2g + 5)).

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Divide. Write your answer in simplest form. $\newline$ $\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)$ $\newline$ ______

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write your answer in simplest form.

\newline

\frac{g- 1}{10g^3 + 25g^2} \div (g- 1)

\newline

______

Rewrite division as multiplication: Rewrite the division as a multiplication by the reciprocal of the second expression. $\newline$ $(g - 1)/(10g^3 + 25g^2) \div (g - 1)$ can be rewritten as $(g - 1)/(10g^3 + 25g^2) \times 1/(g - 1)$ .
Factor out GCF from denominator: Factor out the greatest common factor (GCF) from the denominator of the first fraction. $\newline$ The GCF of $10g^3$ and $25g^2$ is $5g^2$ , so factor that out to get $(g - 1)/(5g^2(2g + 5))$ .
Multiply numerators and denominators: Multiply the numerators and the denominators of the two fractions. $(g - 1)/(5g^2(2g + 5)) \times 1/(g - 1) = (g - 1) \cdot 1 / (5g^2(2g + 5) \cdot (g - 1))$ .
Cancel out terms: Cancel out the $(g - 1)$ terms in the numerator and the denominator. $\newline$ After canceling, the expression simplifies to $\frac{1}{5g^2(2g + 5)}$ .