# How do you simplify the expression ((x^2-4x-32)/(x+1))/((x^2+6x+8)/(x^2-1))?

Dec 26, 2016

The answer is $= \frac{\left(x - 1\right) \left(x - 8\right)}{x + 2}$

#### Explanation:

Let's do some factorisations

${x}^{2} - 4 x - 32 = \left(x + 4\right) \left(x - 8\right)$

${x}^{2} + 6 x + 8 = \left(x + 2\right) \left(x + 4\right)$

${x}^{2} - 1 = \left(x + 1\right) \left(x - 1\right)$

Therefore,

((x^2-4x-32)/(x+1))/((x^2+6x+8)/(x^2-1))=(((x+4)(x-8))/((x+1)))/(((x+2)(x+4))/((x+1)(x-1))

$= \frac{\cancel{x + 4} \left(x - 8\right)}{\cancel{x + 1}} \cdot \frac{\cancel{x + 1} \left(x - 1\right)}{\left(x + 2\right) \cancel{x + 4}}$

$= \frac{\left(x - 1\right) \left(x - 8\right)}{x + 2}$