Solve (x-1)/(sqrt x + 1) = 4 + (sqrt x - 1)/2

$\frac{x , - ,1 }{\sqrt x , + , 1}$ = 4 + $\frac{\sqrt x , - , 1}{2}$

or, $\frac{x , - ,1 }{\sqrt x , + , 1} \times \frac{\sqrt x , - , 1}{\sqrt x , - , 1}$ = $\frac{7 , + , \sqrt x}{2}$

or, $\frac{x\sqrt x , - , x , - , \sqrt x , + , 1}{x , - ,1}$ = $\frac{7 , + , \sqrt x}{2}$

or, $2x\sqrt x , - , 2x , - , 2\sqrt x , + , 2$ = 7x + $x\sqrt x$ - 7 - $\sqrt x$

or, $x\sqrt x , - , 9x , - , \sqrt x , + , 9$ = 0

or, $\sqrt x$(x - 1) - 9(x - 1) = 0

or, (x - 1)($\sqrt x$ - 9) = 0

Either, x = 1 (Not possible)

OR, $\sqrt x$ = 9

Squaring on both sides,

or, $(\sqrt x)^2$ = 9

∴ x = 81

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