Question

In the following exercises, multiply.

$\frac{6p^2-6p}{p^2+7p-18}·\frac{p^2-81}{3p^2-27p}$

Short answer

The required answer is$\frac{2\left(p-1\right)}{p-2}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{6p^2-6p}{p^2+7p-18}·\frac{p^2-81}{3p^2-27p}$

Step 2. Simplify the expression.

$\frac{6p^2-6p}{p^2+7p-18}·\frac{p^2-81}{3p^2-27p}$

Factor the numerator and denominator completely,

$\frac{6p\left(p-1\right)}{\left(p+9\right)\left(p-2\right)}·\frac{\left(p+9\right)\left(p-2\right)}{3p\left(p-9\right)}$

Multiply the numerators and denominators,

$\frac{2·3p\left(p-1\right)\left(p+9\right)\left(p-2\right)}{3p\left(p+9\right)\left(p-2\right)\left(p-9\right)}$

Simplify by dividing out common factors,

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