What is the simplified form of (x-3)/(x^2+x-12) * (x+4)/(x^2 + 8x + 16)?

Jun 12, 2018

$\frac{1}{x + 4} ^ 2$

Explanation:

First, factor the fractions:

$\frac{x - 3}{{x}^{2} + x - 12} \cdot \frac{x + 4}{{x}^{2} + 8 x + 16}$

$\frac{x - 3}{\left(x - 3\right) \left(x + 4\right)} \cdot \frac{x + 4}{\left(x + 4\right) \left(x + 4\right)}$

Now, combine them:

$\frac{\left(x - 3\right) \left(x + 4\right)}{\left(x - 3\right) {\left(x + 4\right)}^{3}}$

$\frac{\cancel{\left(x - 3\right)} \cancel{\left(x + 4\right)}}{\cancel{\left(x - 3\right)} {\left(x + 4\right)}^{\cancel{3} \textcolor{w h i t e}{\text{.}} \textcolor{red}{2}}}$

$\frac{1}{x + 4} ^ 2$

Or if you want to expand it back out:

$\frac{1}{{x}^{2} + 8 x + 16}$