Question

Determine a and b, if √7+√5/√7-√5 - √7-√5/√7+√5 = a+√35b

Answer 1

On rationalisation of Lhs we get
(1+2rot35) /2
=1/2+rot35
Therefore a=1/2 and b=1..

Answer 2

$\frac{ \sqrt{7} + \sqrt{5} }{ \sqrt{7} - \sqrt{5} } - \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$
$\frac{ {( \sqrt{7} + \sqrt{5} ) }^{2} {( \sqrt{7} - \sqrt{5} ) }^{2} }{ { \sqrt{7} }^{2} - { \sqrt{5} }^{2} }$
$\frac{4 \sqrt{35} }{2}$
$2 \sqrt{35}$
On simplification this will come..

Hence,
a = 0
b= 2