SOLUTION: Describe the vertical asymptote(s) and hole(s) for the graph of y = (x-5)/(x^2+4x+3) asymptotes: x=-3,-1 and no holes asymptotes: x=-3 and hole: x=-5 asymptotes: x=-3,-1 and

Algebra ->  Rational-functions -> SOLUTION: Describe the vertical asymptote(s) and hole(s) for the graph of y = (x-5)/(x^2+4x+3) asymptotes: x=-3,-1 and no holes asymptotes: x=-3 and hole: x=-5 asymptotes: x=-3,-1 and       Log On


   

Question 715969: Describe the vertical asymptote(s) and hole(s) for the graph of y = (x-5)/(x^2+4x+3)
asymptotes: x=-3,-1 and no holes
asymptotes: x=-3 and hole: x=-5
asymptotes: x=-3,-1 and hole:x=-5
asymptotes: x=-5 and hole: x=-3
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
y = %28x-5%29%2F%28x%5E2%2B4x%2B3%29

Factor the denominator:

y = %28x-5%29%2F%28%28x%2B3%29%28x%2B1%29%29

There are no holes because the numerator and the denominator
have no common factors.

Therefore the equations of the vertical asymptotes are found 
by setting the denominator = 0

(x+3)(x+1) = 0

x+3=0;  x+1=0
  x=-3;   x=-1

It has x-intercept (5,0) and y-intercept (0,-5%2F4).
The green lines are the vertical asymptotes:



Edwin