Question

What is the product of the rational expressions below?

$\frac{4x}{x+6}·\frac{x-8}{x-6}$

• A. $\frac{4x^2-32}{x^2}$
• B. $\frac{4x^2-32}{x^2-12}$
• C. $\frac{4x^2-32x}{x^2-36}$
• D. $\frac{4x^2-8}{x^2-36}$

Answer 1

The correct option is C

$\frac{4x^2-32x}{x^2-36}$

Explanation for the correct option:

Step-1: Multiplication of algebraic expression:

Given product of expression is $\frac{4x}{x+6}·\frac{x-8}{x-6}$.

for simplifying this, multiply the numerator with numerator and denominator with denominator.

$\Rightarrow \frac{4x}{x+6}·\frac{x-8}{x-6}=\frac{4x\left(x-8\right)}{\left(x+6\right)\left(x-6\right)}$

Step-2: Use the identity:

Using identity expression $\left(a-b\right)\left(a+b\right)=a^2-b^2$

$\begin{array}{rcl}& \Rightarrow & \frac{4x}{x+6}·\frac{x-8}{x-6}=\frac{4x\left(x-8\right)}{\left(x+6\right)\left(x-6\right)}\\ & =& \frac{4x^2-32x}{x^2-6^2}\\ & =& \frac{4x^2-32x}{x^2-36}\end{array}$

Therefore, the correct answer is option $\left(C\right)$.