Question 28
Let $n$ be the positive integer such that
$$\frac1{9\sqrt{11}+11\sqrt9}+\frac1{11\sqrt{13}+13\sqrt{11}}+\frac1{13\sqrt{15}+15\sqrt{13}}+\cdots+\frac1{n\sqrt{n+2}+(n+2)\sqrt n}=\frac19.$$
Find $n$.
$$\frac1{9\sqrt{11}+11\sqrt9}+\frac1{11\sqrt{13}+13\sqrt{11}}+\frac1{13\sqrt{15}+15\sqrt{13}}+\cdots+\frac1{n\sqrt{n+2}+(n+2)\sqrt n}=\frac19.$$
Find $n$.