SOLUTION: How do I find all the asymptotes of G(x)=(x^3-1)/(x+x^2)?

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Question 52506: How do I find all the asymptotes of G(x)=(x^3-1)/(x+x^2)?
Found 2 solutions by stanbon, Nate:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find all the asymptotes of G(x)=(x^3-1)/(x+x^2)?
Vertical asymptotes occur where the denominator is zero, as follows:
x+x^2=0
x(1+x)=0
x=0 or x=-1
Neither of these values makes the numerator zero so you have
vertical asymptotes at x=0 and at x=-1.
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Horizontal asymptotes:
The highest degree of "x" is x^3 and the coefficient of x^3 is "1".
The coefficient of x^3 in the denominator is "0".
The fraction 1/0 is undefined. Therefore there is no horizontal asymptote.
Cheers,
Stan H.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
You can not divide by zero.
This can not be: x^2 + x = 0
x(x + 1) = 0
x = 0 and x = -1
Those are your vertical asymptotes.
There are infinite linear asymptotes. Ex.) y = x + 2
There are no horizontal asymptotes.
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