Question: Solve: $\dfrac{√x +√5}{√x -√5} + \dfrac{√x -√5}{√x +√5} = 4$

Solution:
Given,

$\dfrac{√x +√5}{√x -√5} + \dfrac{√x -√5}{√x +√5} = 4$

$or, \dfrac{(√x +√5)(√x +√5) + (√x -√5)(√x -√5)}{(√x)² - (√5)²} = 4$

$or, \dfrac{(√x)² + 2×√x×√5 + (√5)² + (√x)² -2×√x*√5 +(√5)²}{x -5} = 4$

$or, x + 2\sqrt{5x} + 5 + x -2\sqrt{5x} + 5 = 4(x -5)$

$or, 2x +10 +0 = 4x -20$

$or, 20+10 = 4x -2x$

$or, 30 = 2x$

$or, 2x = 30$

$or, x = \dfrac{30}{2}$

$\therefore x = 15$
= Answer