Question

Simplify$\frac{4b^2+7b-2}{1-b^2}·\frac{b^2-2b+1}{4b^2+15b-4}$.

Short answer

The simplest form of the given expression is

$-\frac{(b-1)(b+2)}{(b+1)(b+4)}.$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{4b^2+7b-2}{1-b^2}·\frac{b^2-2b+1}{4b^2+15b-4}$

Step 2. Simplify

$$\begin{gathered} \frac{4b^2+7b-2}{1-b^2}·\frac{b^2-2b+1}{4b^2+15b-4}=\frac{(4b-1)(b+2)}{-(b-1)(b+1)}·\frac{(b-1)(b-1)}{(4b-1)(b+4)} \\ =-\frac{(b+2)}{(b+1)}·\frac{(b-1)}{(b+4)} \\ =-\frac{(b-1)(b+2)}{(b+1)(b+4)} \end{gathered}$$

Hence, the simplified expression is$-\frac{(b-1)(b+2)}{(b+1)(b+4)}.$