Question

I can't figure this equation out, help!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

$\frac{4}{2x-1}-\frac{2}{x}=2;\ D:2x-1\neq0\ \wedge\ x\neq0\Rightarrow x\neq\frac{1}{2}\ \wedge\ x\neq0\\\\\frac{4}{2x-1}=2+\frac{2}{x}\\\\\frac{4}{2x-1}=\frac{2x}{x}+\frac{2}{x}\\\\\frac{4}{2x-1}=\frac{2x+2}{x}\\\\cross\ multiply\\\\(2x-1)(2x+2)=4x\\4x^2+4x-2x-2-4x=0\\4x^2-2x-2=0\\4x^2-4x+2x-2=0$

$4x(x-1)+2(x-1)=0\\(x-1)(4x+2)=0\iff x-1=0\ \vee\ 4x+2=0\\x=1\in D\ \vee\ x=-\frac{1}{2}\in D\\\\Solutions:x=-\frac{1}{2}\ or\ x=1.$