Question

The value of $\frac{\sqrt{15}-2}{\sqrt{15}+2}+\frac{\sqrt{15}+2}{\sqrt{15}-2}$ is $3\frac{5}{m}$, then $m$ is:

Answer 1

Taking $LCM$ of the denominator,

$\frac{\left[\right(\sqrt{15}-2\left)\right(\sqrt{15}-2)+(\sqrt{15}+2\left)\right(\sqrt{15}+2\left)\right]}{\left[\right(\sqrt{15}+2)\times (\sqrt{15}-2\left)\right]}$

$=\frac{\left[\right(15-4\sqrt{15}+4)+(15+4\sqrt{15}+4\left)\right]}{(15-4)}$

$=\frac{\left[\right(19-4\sqrt{15})+(19+4\sqrt{5})}{11}$

$=\frac{19+19}{11}=\frac{38}{11}=3\frac{5}{11}$.

Therefore, value of $m$ is $11$.