Question

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

***The answer is 1 and -0.5, but I just can't figure out how to work it out.***

Answer 1

`(4)/(2x-1)-(2)/(x)=2;\ D:2x-1\\eq0\ \wedge\ x\\eq0\Rightarrow x\\eq(1)/(2)\ \wedge\ x\\eq0\\\\(4)/(2x-1)=2+(2)/(x)\\\\(4)/(2x-1)=(2x)/(x)+(2)/(x)\\\\(4)/(2x-1)=(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=-(1)/(2)\in D\\\\Solutions:x=-(1)/(2)\ or\ x=1.`