Question

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

Answer 1

`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`

Answer 2

`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`