Question: Solve: $\dfrac{5y -4}{\sqrt{5y} - 2} = 2 - \dfrac{\sqrt{5y} -3}{2}$

Solution:
Given,

$\dfrac{5y -4}{\sqrt{5y} - 2} = 2 - \dfrac{\sqrt{5y} -3}{2}$

$or, \dfrac{(\sqrt{5y})^2 - 2^2}{\sqrt{5y }-2} = \dfrac{4 - (\sqrt{5y} -3)}{2}$

$or, \dfrac{(\sqrt{5y} +2)(\sqrt{5y} -2)}{\sqrt{5y}-2} = \dfrac{4 - \sqrt{5y} +3}{2}$

$or, \sqrt{5y} + 2 = \dfrac{7 - \sqrt{5y}}{2}$

$or, 2(\sqrt{5y} + 2) = 7 - \sqrt{5y}$

$or, 2\sqrt{5y} + 4 = 7 - \sqrt{5y}$

$or, 2\sqrt{5y} + \sqrt{5y} = 7 -4$

$or, 3\sqrt{5y} = 3$

$or, \sqrt{5y} = \dfrac{3}{3}$

$or, \sqrt{5y} = 1$

$or, \sqrt{5y} = √1$

$or, 5y = 1$

$or, y = \dfrac{1}{5}$
= Answer