# How do you simplify (8+x³) / (x+2)?

Oct 18, 2015

Use the sum of cubes identity: ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$ to find:

$\frac{8 + {x}^{3}}{x + 2} = {x}^{2} - 2 x + 4$ with exclusion $x \ne - 2$

#### Explanation:

$8 + {x}^{3} = {x}^{3} + {2}^{3} = \left(x + 2\right) \left({x}^{2} - 2 x + 4\right)$

So:

$\frac{8 + {x}^{3}}{x + 2} = \frac{\left(x + 2\right) \left({x}^{2} - 2 x + 4\right)}{x + 2} = {x}^{2} - 2 x + 4$

with exclusion $x \ne - 2$