SOLUTION: Where (for what the values of x) does the function -8 (x+62)(x-29)/(x-59)(x-37)(x-29) have A holes? B. Vertical asymptotes?

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Question 1125170: Where (for what the values of x) does the function
-8 (x+62)(x-29)/(x-59)(x-37)(x-29)
have
A holes?
B. Vertical asymptotes?
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
Just some limited help:

Do you see a factor in both the numerator AND the denominator? Yes you do. That is x-29, indicating that x%3C%3E29 and therefore the rational expression has a hole for x at 29.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-%288+%28x%2B62%29%28x-29%29%29%2F%28%28x-59%29%28x-37%29%28x-29%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=-%288+%28x%2B62%29%28x-29%29%29%2F%28%28x-59%29%28x-37%29%28x-29%29%29 which is already factored and you can see there is %28x-29%29 to simplify, that is common factor, means there is a hole at x=29
find y coordinate, plug in x=29
y=-%288+%2829%2B62%29%2829-29%29%29%2F%28%2829-59%29%2829-37%29%2829-29%29%29
y=-%288+%2891%29%280%29%29%2F%28%2887%29%2866%29%280%29%29
y=0
hole is at (29,0)

and vertical asymptotes:
f%28x%29=-%288+%28x%2B62%29%28x-29%29%29%2F%28%28x-59%29%28x-37%29%28x-29%29%29...first simplify

f%28x%29=-%288+%28x%2B62%29%29%2F%28%28x-59%29%28x-37%29%29

I'll find any vertical asymptotes, by setting the denominator equal to zero and solving:
%28x-59%29%28x-37%29=0
and it is
%28x-59%29=0->x=59}
%28x-37%29=0->x=37}
a vertical asymptotes are at x=59, andx=37
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