Question

How do you simplify `\frac { x + 1} { x - 1} = \frac { 2} { 2x - 1} + \frac { 2} { x - 1}`?

Answer 1

I found: `x=3/2`

Explanation:

Let us take `(x-1)(2x-1)` as common denominator and manipulate our fractions to get:

`((x+1)(2x-1))/((x-1)(2x-1))=(2(x-1)+2(2x-1))/((x-1)(2x-1))`

`(2x^2-x+2x-1)/cancel((x-1)(2x-1))=(2x-2+4x-2)/cancel((x-1)(2x-1))`

`2x^2-5x+3=0`

we use the Quadratic Formula:

`x_(1,2)=(5+-sqrt(25-24))/4`
`x_1=(5+1)/4=3/2`
`x_2=(5-1)/4=1` that cannot be used because it will make the denominator `x-1` equal to zero in the original expression!