# How do you simplify  7div(sqrt6 – 5)?

Mar 24, 2018

$\frac{7}{\sqrt{6} - 5} = - 7 \cdot \frac{\sqrt{6} + 5}{19}$

#### Explanation:

[0]$\frac{7}{\sqrt{6} - 5} = \left(7 \cdot \frac{\sqrt{6} + 5}{\left(\sqrt{6} - 5\right) \left(\sqrt{6} + 5\right)}\right)$,
[1]$\frac{7}{\sqrt{6} - 5} = 7 \cdot \frac{\sqrt{6} + 5}{6 - 25}$,
[2]$\frac{7}{\sqrt{6} - 5} = - 7 \cdot \frac{\sqrt{6} + 5}{19}$

Mar 24, 2018

$- \frac{7 \sqrt{6} + 35}{19}$

#### Explanation:

Rationalize the denominator (no radicals) by multiplying the numerator and denominator by $\sqrt{6} + 5$.

7/(sqrt(6)-5 * $\frac{\sqrt{6} + 5}{\sqrt{6} + 5}$

$\frac{7 \sqrt{6} + 35}{-} 19$

$- \frac{7 \sqrt{6} + 35}{19}$