Rational expressions and equations
State the non-permissible values from the original denominators, then simplify or solve, and reject any answer that is one of them.
A worked example
(x² − 9)/(x − 3) = (x − 3)(x + 3)/(x − 3) = x + 3, x ≠ 3. Solving x/(x − 3) − 2 = 3/(x − 3) gives x = 3, which is non-permissible, so there is no solution.
The mistake people actually make
Cancelling a factor does not cancel its restriction: the graph of (x² − 9)/(x − 3) is the line y = x + 3 with a hole at (3, 6).