Question

. If 7+√57−√5−7−√57+√5=+√5, find the values of a and b.

Answer 1

Well, first you need to simplify your expression.
How ? Simple! By rationalising.
(7+√5)/(7-√5) - (7-√5)/7+√5) 
Rationalise both the terms 
(7+√5)² - (7-√5)²/ 49 - 5 = 49 + 14√5 + 5 - 49 + 14√5 - 5/ 44= 28√5/44= 7√5/11 
Now, 7√5/11 = a + (7/11) √5b
On comparison, a = 0b = 1