Question

Simplify the complex rational expression by writing it as a division:

$\frac{{\displaystyle \frac{2}{x^2-1}}}{{\displaystyle \frac{3}{x+1}}}$

Short answer

$\frac{2}{3\left(x-1\right)}$

Step-by-step solution

Step 1. Given information.

The following complex rational expression is given:

$\frac{{\displaystyle \frac{2}{x^2-1}}}{{\displaystyle \frac{3}{x+1}}}$

Step 2. Simplification of the rational expression.

Rewrite the fraction as a division:

$\frac{2}{x^2-1}÷\frac{3}{x+1}$

Rewrite as the product of the first and the reciprocal of the second:

$\frac{2}{x^2-1}.\frac{x+1}{3}$

Factor the terms whenever possible:

$\frac{2}{\left(x-1\right).\left(x+1\right)}.\frac{\left(x+1\right)}{3}$

Multiply:

$\frac{2.\left(x+1\right)}{\left(x-1\right).\left(x+1\right).3}$

Remove the common factors present in the numerator and the denominator:

$\frac{2}{3\left(x-1\right)}$