Question

In the following exercises, multiply.

$\frac{28-4b}{3b-3}·\frac{b^2+8b-9}{b^2-49}$

Short answer

The required answer is$-\frac{4\left(b+9\right)}{3\left(b+7\right)}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{28-4b}{3b-3}·\frac{b^2+8b-9}{b^2-49}$

Step 2. Simplify the expression.

$\frac{28-4b}{3b-3}·\frac{b^2+8b-9}{b^2-49}$

Factor the numerator and denominator completely,

$\frac{4\left(7-b\right)}{3\left(b-1\right)}·\frac{\left(b+9\right)\left(b-1\right)}{\left(b+7\right)\left(b-7\right)}$

Multiply the numerators and denominators,

$-\frac{4\left(b-7\right)\left(b+9\right)\left(b-1\right)}{3\left(b-1\right)\left(b+7\right)\left(b-7\right)}$

Simplify by dividing out common factors,

$-\frac{4\left(b+9\right)}{3\left(b+7\right)}$