CPM Homework Help : PCT Problem 8-79

State the coordinates of any holes and the equations of any asymptotes for the function $f(x)=\frac{2x^2+3x-2}{x^2-4}$ .

Step 1:

Factor completely:

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

Step 2:

HOLES or VERTICAL ASYMPTOTES occur when the denominator $=0$ . In this case $x=−2$ is where a hole occurs because the factor divides evenly into the numerator. $x=2$ is a vertical asymptote because the factor does not divide evenly into the numerator.

Step 3:

If you were to rewrite this equation using polynomial division, what would the "whole" term(s) be? This will tell you the horizontal or slant asymptote.