# RATL 3 | Lesson 4 | Explore (Finding Holes)

Factor the following rational functions:

a) $$f(x)=\Large \frac{3x^2-12x-15}{x^2-3x-10}$$

b) $$f(x)=\Large \frac{x^2-9}{x-3}$$

c) $$f(x)=\Large \frac{4x^2+8x-12}{x^2-4x-21}$$

Once factored, note that binomials that are both in the numerator and the denominator can be divided out as a factors of one. Setting those factors equal to zero show you where the “holes” are in the function when it is graphed. For example, for function b), $$\Large \frac{(x-3)}{(x-3)}$$ can be divided out of the function. So there is a hole where x is equal to three. Evaluating for three in the simplified version of the function, they y-value would have been 6. So, the hole is at $$(3,6)$$ on the graph.

Check solutions here.