Question 219068
what are the roots and asymptotes of f(x)=x^2-4x-5 over x^2+2x+1
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Roots?
solve x^2-4x-5 = 0
(x-5)(x+1) = 0
x = 5 or x = -1
Those are the roots.
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Asymptotes?
solve x^2 + 2x +1 = 0
(x+1)(x+1) = 0
x = -1 or x = -1
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Comment: Since numerator and denominator have the factor x+1,
x = -1 is not a root and not an asymptote value.  It is a hole.
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So x = 5 is a root and there are no vertical asymptotes.
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The horizontal asymptote is y = x^2/x^2 = 1
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Cheers,
Stan H.