How do you simplify  [sqrt2 + sqrt 5] / [sqrt2 – sqrt5]?

Sep 8, 2015

$- \frac{7 + 2 \sqrt{10}}{3}$

Explanation:

We can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator:

$\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$

$= \frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}} \times \frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} + \sqrt{5}}$

$= \frac{2 + 2 \sqrt{10} + 5}{2 - 5}$

$= - \frac{7 + 2 \sqrt{10}}{3}$