(x -25)/(√x -5) = 9 | Surds - Solve | SciPiPupil

Question: Solve: $\dfrac{x -25}{√x -5} = 9$

Solution:

Given,

$\dfrac{x -25}{√x -5} = 9$

$or, \dfrac{(√x)^2 - (5)^2}{√x -5} = 9$

$or, \dfrac{(√x +5)(√x -5)}{(√x -5)} = 9$

$or, √x +5 = 9$

$or, √x = 9-5$

$or, √x = 4$

[ Squaring both sides ]

$or, (√x)^2 = 4^2$

$\therefore x = 16$

= Answer