Question

Find all values of $x$ such that
\[\frac{2x}{x + 2} = \frac{x - 3}{x - 4}.\]If you find more than one value, then list your solutions, separated by commas.

Answer 1

Cross-multiply (noting x ≠ −2, 4):
2x(x − 4) = (x − 3)(x + 2)
2x^2 − 8x = x^2 − x − 6
x^2 − 7x + 6 = 0
(x − 1)(x − 6) = 0

So x = 1 or x = 6.