# How do you simplify (-2+sqrt8)/(-3-sqrt2)?

Jun 9, 2015

Multiply numerator and denominator by $\left(3 - \sqrt{2}\right)$, expand, group, combine and eliminate common factors to get:

$\frac{- 2 + \sqrt{8}}{- 3 - \sqrt{2}} = 1 - \sqrt{2}$

#### Explanation:

$\frac{- 1 + \sqrt{8}}{- 3 - \sqrt{2}}$

$= \frac{1 - \sqrt{8}}{3 + \sqrt{2}}$

$= \frac{1 - \sqrt{8}}{3 + \sqrt{2}} \cdot \frac{3 - \sqrt{2}}{3 - \sqrt{2}}$

$= \frac{\left(1 - 2 \sqrt{2}\right) \cdot \left(3 - \sqrt{2}\right)}{{3}^{2} - {\left(\sqrt{2}\right)}^{2}}$

[using the difference of squares identity: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$]

$= \frac{3 - \sqrt{2} - 6 \sqrt{2} + 2 {\left(\sqrt{2}\right)}^{2}}{9 - 2}$

$= \frac{3 - 7 \sqrt{2} + 4}{7}$

$= \frac{7 - 7 \sqrt{2}}{7}$

$= 1 - \sqrt{2}$