How do you simplify (x+1)/(x-1)=2/(2x-1)+2/(x-1)?

2 Answers

x=3/2

Explanation:

Given that

\frac{x+1}{x-1}=\frac{2}{2x-1}+\frac{2}{x-1}

\frac{x+1}{x-1}-\frac{2}{2x-1}-\frac{2}{x-1}=0

\frac{(x+1)(2x-1)-2(x-1)-2(2x-1)}{(x-1)(2x-1)}=0

\frac{2x^2-5x+3}{(x-1)(2x-1)}=0

\frac{2x^2-2x-3x+3}{(x-1)(2x-1)}=0

\frac{2x(x-1)-3(x-1)}{(x-1)(2x-1)}=0

\frac{(2x-3)(x-1)}{(x-1)(2x-1)}=0

\frac{2x-3}{2x-1}=0

2x-3=0\quad \forall \ x\ne1/2

x=3/2

Jun 26, 2018

x=3/2 or 1.5

Explanation:

we have
(x+1)/(x-1)=(2/(2x-1))+(2/(x-1))
shifting (2/(x-1)) to other side
=>(x+1)/(x-1)-(2/(x-1))=(2/(2x-1))
=>(x+1-2)/(x-1)=(2/(2x-1))
=>cancel(x-1)/cancel(x-1)=(2/(2x-1))
=>2x-1=2; =>x=3/2 or 1.5