Question

What is simplest form of sqrt 2 + sqrt 5 / sqrt 2 - sqrt -5? √2 + √5 / √2 - √-5

Answer 1

Answer:

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

Step-by-step explanation:

we have

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

Simplify

Multiply the expression by  $\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}$

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

Apply difference of squares in the denominator

$\frac{(\sqrt{2}+\sqrt{5})^2}{(\sqrt{2})^2-(\sqrt{5})^2}$

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

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

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