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Formation of Algebraic Expressions

Solve the fol...

Question

Solve the following equation:
$\sqrt{\frac{2 x + 1}{x - 1}} - 2 \sqrt{\frac{x - 1}{2 x + 1}} = 1$

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Solution

$\sqrt{\frac{2 x + 1}{x - 1}} b e t t - \frac{2}{t} = 1 t^{2} - t - 2 = 0 (t - 2) (t - 1) = 0 t = - 1, 2 \sqrt{\frac{2 x + 1}{x - 1}} = - 1 \frac{2 x + 1}{x - 1} = 1 2 x + 1 = x - 1 x = - 2 \sqrt{\frac{2 x + 1}{x - 1}} = 2 \frac{2 x + 1}{x - 1} = 4 2 x + 1 = 4 x - 4 x = \frac{5}{2}$

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