- First factor both the numerator and the denominator.
- Cancel any common factors to reduce the fraction.
- The roots of the reduced
*denominator*give you**vertical asymptotes**; each one is a vertical line. - The roots of the factors that you
*cancelled*give you**holes**(unless you already have a vertical asymptote there); plug each one into the reduced expression to get its other coordinate. - The roots of the reduced
*numerator*give you**horizontal intercepts**(unless you already have a hole there); each one is a point on the horizontal axis. - If you perform
*long division*(or a shortcut) and throw out the remainder, then you get a polynomial; this is the formula for the**other asymptote**(which the graph might cross). - Don't forget the
**vertical intercept**(unless there's a hole there), which works the same way as always.

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