Unit G Summary Question #9 x intercepts of rational functions

To find the x intercepts of rational functions, obviously we have to plug in 0 as our y. For example, x^2-4x-4/ x^2+6x+9. If we plug in zero as our y, then we have a ratio. (0/1)=(x^2-4x-4)/(x^2+6x+9). When we cross multiply, the denominator becomes zero and the numerator factors into (x-2)(x-2). We then set this to zero and our x intercepts is 2 multiplicity 2. The shortcut is basically factoring the numerator and setting it to zero. This makes more sense because if you were to find the x intercept the long way, then you would still get to this point but not until after you've done some unnecessary work. It takes less time and is easy to do.