Question

Write an equation that has a hole at x = 4 and a vertical asymptote at x = -3.

Answer 1

This has to be a rational equation in order to have those characteristics...in other words a fraction. One such equation would look like this:
x^2 - 2x - 8/x^2 - x - 12.  When you factor both the numerator and the denominator you get (x-4)(x+2)/(x-4)(x+3).  Because the (x-4) is in both the top and the bottom of the fraction, you can cancel them out, which makes that (x-4) a removable discontinuity.  The (x+3) exists as a vertical asymptote.