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

Factor the following rational functions:

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

$$f(x)=\Large\frac{3(x+1)(x-5)}{(x+2)(x-5)}$$

There is a hole at $$x = 5$$.

b) $$f(x)=\Large \frac{x^2-9}{x-3}$$

$$f(x) = \Large\frac{(x+3)(x-3)}{x-3}$$

There is a hole at $$x = 3$$.

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

$$f(x) = \Large\frac{4(x +3)(x – 1)}{(x + 3)(x – 7)}$$

There is  hole at $$x = -3$$.