Question

Simplify:

$\frac{\sqrt{4}+\sqrt{5}}{\sqrt{4}-\sqrt{5}}+\frac{\sqrt{4}-\sqrt{5}}{\sqrt{4}+\sqrt{5}}=-m$ then the value of $m$ is

Answer 1

$Werationalizethedenominatorswiththerespectivefactor,\frac{\sqrt{5}+\sqrt{4}}{\sqrt{4}-\sqrt{5}}\times \frac{\sqrt{5}+\sqrt{4}}{\sqrt{5}+\sqrt{4}}+\frac{\sqrt{4}-\sqrt{5}}{\sqrt{5}+\sqrt{4}}\times \frac{-\sqrt{5}+\sqrt{4}}{-\sqrt{5}+\sqrt{4}}=\frac{5+4+2\sqrt{20}+5+4-2\sqrt{20}}{4-5}=\frac{-18}{1}$

$=-18$

$\therefore m=18$