Question

Multiply the following and write your answer in lowest terms: $\frac{3x^2+2x-1}{x^2-x-2}\times \frac{2x^2-3x-2}{3x^2+5x-2}$

• A. $\frac{2x+1}{x+2}$
• B. $\frac{2x-1}{x+2}$
• C. $\frac{2x+1}{x-2}$
• D. None of these

Answer 1

The correct option is A $\frac{2x+1}{x+2}$

The given expression $\frac{3x^2+2x-1}{x^2-x-2}\times \frac{2x^2-3x-2}{3x^2+5x-2}$can be simplified as shown below:

$=\frac{3x^2+2x-1}{x^2-x-2}\times \frac{2x^2-3x-2}{3x^2+5x-2}$

$=\frac{3x^2+3x-x-1}{x^2-2x+x-2}\times \frac{2x^2-4x+x-2}{3x^2+6x-x-2}$

$=\frac{3x(x+1)-1(x+1)}{x(x-2)+1(x-2)}\times \frac{2x(x-2)+1(x-2)}{3x(x+2)-1(x+2)}$

$=\frac{(3x-1)(x+1)}{(x+1)(x-2)}\times \frac{(2x+1)(x-2)}{(3x-1)(x+2)}$

$=\frac{(3x-1)(x+1)(2x+1)(x-2)}{(x+1)(x-2)(3x-1)(x+2)}$

$=\frac{2x+1}{x+2}$

Hence, $\frac{3x^2+2x-1}{x^2-x-2}\times \frac{2x^2-3x-2}{3x^2+5x-2}=\frac{2x+1}{x+2}$.