Correct Answer: $\sqrt{2}+1$

Solution : Given: The expression is $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div \frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}$.
Take $\sqrt2$ common in the term $\frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}$, we get,
$\frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}–\sqrt{10}}=\frac{\sqrt2}{\sqrt2}\times\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}}=\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}}$
The expression can be written as $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \div\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} +\frac{\sqrt{10}}{\sqrt{5}}$
= $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}–\sqrt{5}} \times\frac{\sqrt{7}–\sqrt{5}}{\sqrt{7}+\sqrt{5}} +\frac{\sqrt{10}}{\sqrt{5}}$
= $1+\sqrt2$
= ${\sqrt{2}}+1$
Hence, the correct answer is ${\sqrt{2}}+1$.