What is the value of $$\frac{{\sqrt 7 + \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} \div \frac{{\sqrt {14} + \sqrt {10} }}{{\sqrt {14} - \sqrt {10} }} + \frac{{\sqrt {10} }}{{\sqrt 5 }}?$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{\sqrt 7 + \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} \div \frac{{\sqrt {14} + \sqrt {10} }}{{\sqrt {14} - \sqrt {10} }} + \frac{{\sqrt {10} }}{{\sqrt 5 }} \cr & = \frac{{\sqrt 7 + \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} \div \frac{{\frac{{\sqrt {14} + \sqrt {10} }}{{\sqrt 2 }}}}{{\frac{{\sqrt {14} - \sqrt {10} }}{{\sqrt 2 }}}} + \frac{{\sqrt {10} }}{{\sqrt 5 }} \cr & = \frac{{\sqrt 7 + \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} \times \frac{{\sqrt 7 - \sqrt 5 }}{{\sqrt 7 + \sqrt 5 }} + \sqrt 2 \cr & = 1 + \sqrt 2 \cr} $$