Question

Multiply the following and write your answer in lowest terms: $\frac{x^2-2x}{x+2}\times \frac{3x+6}{x-2}$

• A. $3x$
• B. $x$
• C. $2x$
• D. None of these

Answer 1

The correct option is A $3x$

The given expression $\frac{x^2-2x}{x+2}\times \frac{3x+6}{x-2}$ can be simplified as shown below:

$=\frac{x^2-2x}{x+2}\times \frac{3x+6}{x-2}$

$=\frac{x(x-2)}{x+2}\times \frac{3(x+2)}{x-2}$

$=\frac{3x(x-2)(x+2)}{(x+2)(x-2)}$

$=3x$

Hence, $\frac{x^2-2x}{x+2}\times \frac{3x+6}{x-2}=3x$.