Question

solve the equation and the answer must be 4 and -1​

Answer 1

$let \: \sqrt{ \frac{x}{x - 3} } be \: {y}^{2} \\ and \: \: \sqrt{ \frac{x - 3}{x } \: } \: be \frac{1}{y {}^{2} } \\ now \\ y \: + \frac{1}{y} = 2 \\ y {}^{2} - 2y + 1 = 0 \\y {}^{2} - y - y + 1 = 0 \\ y(y - 1) - 1(y - 1) = 0 \\ y = - 1 \\ hence \: y {}^{2} = ( - 1) {}^{2} = 1$