Question

Solve for all values of x.
x, minus, start fraction, 3, divided by, x, minus, 9, end fraction, equals, start fraction, 7, divided by, x, minus, 9, end fraction
x−
x−9
3
​
=
x−9
7

Answer 1

Solve x − 3/(x − 9) = 7/(x − 9), noting x ≠ 9.

Multiply both sides by (x − 9):
x(x − 9) − 3 = 7
x^2 − 9x − 3 − 7 = 0
x^2 − 9x − 10 = 0

Factor:
(x − 10)(x + 1) = 0

So x = 10 or x = −1. Both are allowed (not 9), and they satisfy the original equation.