Question

find the x values where the rational function has a hole or vertical asymptote.

1. $k(x)=\frac{(x + 7)(x + 2)^3}{(x + 1)(x + 2)^2}$

hole(s):
vertical asymptote(s):

Explanation:

Step1: Identify common factors for holes

A hole occurs when there is a common factor in the numerator and denominator. The common factor here is $(x + 2)^2$. Set $x+2 = 0$, so $x=-2$.

Step2: Identify non - common factors for vertical asymptotes

The non - common factor in the denominator is $(x + 1)$. Set $x + 1=0$, so $x=-1$.

Answer:

Hole(s): $x=-2$
Vertical Asymptote(s): $x=-1$