Question

Simplify:
If $\frac{3}{5-\sqrt{3}}+\frac{2}{5+\sqrt{3}}$ is $\frac{25+\sqrt{m}}{22}$, then $m$ is ?

Answer 1

We rationalize the denominators with the respective factor $\frac{3}{5-\sqrt{3}}\ast \frac{5+\sqrt{3}}{5+\sqrt{3}}+\frac{2}{5+\sqrt{3}}\ast \frac{5-\sqrt{3}}{5-\sqrt{3}}=\frac{15+3\sqrt{3}+10-2\sqrt{3}}{25-3}=\frac{25+\sqrt{3}}{22}$