The simplified form of 2 7 + 5 + 7 12 - 5 - 5 12 - 7 is = ?

Answer: Option D

$$\frac{2}{\sqrt{7}+\sqrt{5}}+\frac{7}{\sqrt{12}-\sqrt{5}}-\frac{5}{\sqrt{12}-\sqrt{7}}$$
$$=\frac{2}{\sqrt{7}+\sqrt{5}}\times$$  $$\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}-\sqrt{5}}+$$  $$\frac{7}{\sqrt{12}-\sqrt{5}}\times$$  $$\frac{\sqrt{12}+\sqrt{5}}{\sqrt{12}+\sqrt{5}}-$$  $$\left(\frac{5}{\sqrt{12}-\sqrt{7}}\times \frac{\sqrt{12}+\sqrt{7}}{\sqrt{12}+\sqrt{7}}\right)$$
$$=\frac{2\left(\sqrt{7}-\sqrt{5}\right)}{2}+$$   $$\frac{7\left(\sqrt{12}+\sqrt{5}\right)}{7}-$$   $$\frac{5\left(\sqrt{12}+\sqrt{7}\right)}{5}$$
$$\begin{array}{rl}& =\sqrt{7}-\sqrt{5}+\sqrt{12}+\sqrt{5}-\sqrt{12}-\sqrt{7}\\ & =0\end{array}$$