Question

Solve for all values of x.
x, minus, start fraction, 2, x, divided by, x, minus, 2, end fraction, equals, start fraction, 5, divided by, x, minus, 2, end fraction
x−
x−2
2x
​
=
x−2
5

Answer 1

Interpret the equation as
x − (2x)/(x − 2) = 5/(x − 2), with x ≠ 2.

Multiply both sides by x − 2:
x(x − 2) − 2x = 5
x^2 − 2x − 2x = 5
x^2 − 4x − 5 = 0

Factor:
(x − 5)(x + 1) = 0

So x = 5 or x = −1. Both are allowed (neither equals 2), and they satisfy the original equation.