how do you solve for x in this problem? : (2/x-1) +1= (2/x²- x)?

Question

I do not understand how to simply solve for x... Please help!

Answer 1

It's unclear what are the denominators and the numerators, but I'll try.

(2/x-1) +1 = (2/x²- x)
...mult the 1 on the left by (x-1)/(x-1)
(2 + (x - 1))/(x-1) = (2/x²- x)
...factor out an x from the denominator on the right
(2 + (x - 1))/(x-1) = 2/(x(x - 1))
...and add the integers on the left
(1 + x)/(x-1) = 2/(x(x - 1))
...multiply both sides by x - 1
1 + x = 2/x
...multiply both sides by x
x² + x = 2
...subtract 2 from both sides
x² + x - 2 = 0
...factor
(x - 2)(x + 1) = 0
...resolve
x = -1, 2

Answer 2

x = 2

Answer 3

Rearange to obtain the form f(x)=0. Then solve as a quadratic, using the formula, or factorisation if possible.