SOLUTION: where does the rational function f(x)=7 (x+54)(x-40)/(x+56)(x+87)(x-55) holes and vertical asymptotes?

Algebra ->  Rational-functions -> SOLUTION: where does the rational function f(x)=7 (x+54)(x-40)/(x+56)(x+87)(x-55) holes and vertical asymptotes?      Log On


   

Question 1125161: where does the rational function
f(x)=7 (x+54)(x-40)/(x+56)(x+87)(x-55)
holes and vertical asymptotes?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29
holes:
To find the holes in a rational function, you must factor the numerator and denominator of the rational function and see if there are any common factors, then simplify it. If there is the same factor in the numerator and denominator, there is a hole.
you are given
f%28x%29=%287+%28x%2B54%29%28x-40%29%29%2F%28%28x%2B56%29%28x%2B87%29%28x-55%29%29 which is already factored and you can see there is nothing to simplify, there are no common factors, means there are no+holes


and vertical asymptotes:

I'll find any vertical asymptotes, by setting the denominator equal to zero and solving:
%28x%2B56%29%28x%2B87%29%28x-55%29=0
and it is
%28x%2B56%29=0->x=-56
%28x%2B87%29=0->x=-87
%28x-55%29=0->x=55
a vertical asymptotes are at x=-56,x=-87,and x=55