Question

What is the quotient of the rational expression below?

Answer 1

Answer:

first answer

Step-by-step explanation:

Hello, you know that

$\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\cdot \dfrac{d}{c}$

So, the quotient we need to estimate is

$\begin{aligned}\dfrac{x^2-36}{x+8}\cdot\dfrac{4x+32}{x^2+12x+36}&=\dfrac{x^2-6^2}{x+8}\cdot \dfrac{4(x+8)}{(x+6)^2}\\\\&=\dfrac{4(x-6)(x+6)}{(x+6)^2}\\\\&=\dfrac{4(x-6)}{x+6}\end{aligned}$

Thank you