Question

Solve for all values of x.
x, minus, start fraction, x, plus, 7, divided by, x, minus, 10, end fraction, equals, start fraction, 5, divided by, x, minus, 10, end fraction
x−
x−10
x+7
​
=
x−10
5

Answer 1

Solve
x - (x+7)/(x-10) = 5/(x-10), with x ≠ 10.

Multiply both sides by (x-10):
x(x-10) - (x+7) = 5
x^2 - 10x - x - 7 = 5
x^2 - 11x - 12 = 0
Factor: (x - 12)(x + 1) = 0

So x = 12 or x = -1. Both are allowed (≠ 10), so the solutions are x = 12, -1.