# How do you find the vertical, horizontal or slant asymptotes for #y = (8 x^2 + x - 2)/(x^2 + x - 72)#?

The vertical asymptotes are

and the horizontal asymptote is

There is no slant asymptote because the degree of the polynomial in the denominator and numerator are the same.

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To find the vertical asymptotes, factor the denominator and identify any values of ( x ) that make the denominator zero. These values will be the vertical asymptotes.

To find the horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is ( y = 0 ). If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote.

To find the slant asymptote, perform polynomial long division or synthetic division to divide the numerator by the denominator. The quotient obtained will represent the equation of the slant asymptote. If the division results in a remainder, there is no slant asymptote.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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