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Answer 1

Answer:

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Step-by-step explanation:

$to \: find = \\ value \: of \: x \\ \\ so \: here \: given \: equation \: is \\ \\ \frac{x - 1}{ \sqrt{x} + 1} = 1 \\ \\ so \: let \: then \\ \sqrt{x} = y \\ \\ hence \: then \\ x = y {}^{2} \\ \\ thus \: then \: accordingly \\ \\ \frac{y {}^{2} - 1}{y + 1} = 1 \\ \\ y {}^{2} - 1 = y + 1 \\ \\ y {}^{2} - y - 2 = 0 \\ \\ y {}^{2} - 2y + y - 2 = 0 \\ \\ y(y - 2) + 1(y - 2) = 0 \\ \\ (y - 2)(y + 1) = 0 \\ \\ y - 2 = 0 \: \: or \: \: y + 1 = 0 \\ \\ y = 2 \: \: or \: \: y = - 1$

$thus \: resubstituting \: now \\ we \: get \\ \\ x = y {}^{2} \\ if \: y = 2 \\ \\ x = 4 \\ \\ if \: y = - 1 \\ \\ x = 1 \\ \\ henceforth \\ x = 4 \: \: or \: \: x = 1$