There are two ways to find the x-intercepts for a rational function. There is a long way and a shortcut way. the long way is illustrated below. First we set our function equal to zero. Then we multiply and the denominator will get canceled. Next, we factor the polynomial. Once we have the factors we set them equal to zero and we put them into ordered pairs to get our x-intercepts. The shortcut way is similar to the long way but it has less steps. In the short cut we simply set the numerator equal to zero, factor it, solve and we have our x-intercepts. The shortcut way makes sense because when we cancel the denominator in the long way, we only concentrate on the numerator. In the shortcut we immediately start working with the numerator so that's why the shortcut makes sense.
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