If f(x) = 2x2 – x – 6 and g(x) = x2 – 4 find f(x) ÷ g(x)

When you divide these, factor both the numerator and the denominator to see if anything cancels out.  That's the best way to do it.  Easier than long division of polynomials, although it can also be done that way.  Factoring both the numerator and denominator gives you this:  .  The (x-2) factor cancels out in the top and bottom leaving you with just .  That's your answer.