Question

√(2x+1/x-1) - 2√(x-1/2x+1)=1

Answer 1

$\sqrt{\frac{2x+1}{x-1}}-2\sqrt{\frac{x-1}{2x+1}}=1\\\frac{3}{\sqrt{2x^2-x-1}}=1\\9=2x^2-x-1\\2x^2-x-10=0\Rightarrow x=\left \{ -2;\frac{5}{2} \right \}\\\frac{2x+1}{x-1}\geq 0\Rightarrow x=\frac{5}{2}$