What is the value of 7 + 5 7 - 5 ÷ 14 + 10 14 - 10 + 10 5 ?

Answer: Option A

$$\begin{array}{rl}& \frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}÷\frac{\sqrt{14}+\sqrt{10}}{\sqrt{14}-\sqrt{10}}+\frac{\sqrt{10}}{\sqrt{5}}\\ & =\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}÷\frac{\frac{\sqrt{14}+\sqrt{10}}{\sqrt{2}}}{\frac{\sqrt{14}-\sqrt{10}}{\sqrt{2}}}+\frac{\sqrt{10}}{\sqrt{5}}\\ & =\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}\times \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}+\sqrt{2}\\ & =1+\sqrt{2}\end{array}$$