Question

Use factoring to simplify the expression x^2-x-6/x-3 assume that x does not equal 3

Answer 1

This works out beautifully.  You COULD use long division here, but since your numerator is a quadratic, your first instinct should be to try and factor it.  If you factor it, it works out to be (x - 3)(x + 2).  Now it just so happens that when you do that, the (x - 3) in the numerator will cancel with the (x - 3) in the denominator leaving you with one sad and lonely (x + 2) as your answer.