describe all asymptotes in the graph of (x^2-1)y=x^2-4

Re: asymptotes

describe all asymptotes in the graph of (x^2-1)y=x^2-4
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No calculus involved. Rearrange the equation to solve for y.
Factor the numerator and denominator.
Cancel any common factors between numerator and denominator.
Solve for x in remaining denominator factors when factors are set equal to zero.
These values of x are where vertical asymptotes will occur.
 
For horizontal asymptote - you need to investigate the value of y as x -> infinity. To do that, rearrange your equation

\(\displaystyle y = f(x)\)

in such a way that, it becomes

\(\displaystyle y = C + \frac{f_1(x)}{f_2(x)}\\)

where the degree of

\(\displaystyle f_1(x)\)

is lower than that of

\(\displaystyle f_2(x)\).

In that case your horizontal asymptote is

y = C
 
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