You can simplify the LHS by rationalizing the denominator (multiplying by the conjugate over the conjugate and using difference of perfect squares on the bottom to eliminate square roots).
$\displaystyle \frac{1}{\sqrt{n}+\sqrt{n+1}}=\frac{1}{\sqrt{n}+\s qrt{n+1}} \times \frac{\sqrt{n}-\sqrt{n+1}}{\sqrt{n}-\sqrt{n+1}}=\frac{\sqrt{n}-\sqrt{n+1}}{n-(n+1)}$
$\displaystyle =\frac{\sqrt{n}-\sqrt{n+1}}{-1}$
$\displaystyle =\sqrt{n+1}-\sqrt{n}$
i.e.
$\displaystyle \frac{1}{\sqrt{4}+\sqrt{5}}=\sqrt{5}-\sqrt{4}$
See if you can use this to solve the problem