Determine the vertical asymptotes of a rational function by factoring the rational function to its most basic terms. This can be done by grouping, or using the distributive property and factoring greatest common factor. Then, determine what terms in the denominator would solve to 0. These are the asymptotes.
- Factor the rational expression
Starting with an example expression such as (x^2 + x -12)/(x^2 - 3x - 10), factor the expression down to basic terms. Determine which factors of the constant would result in the middle term when using the FOIL method to multiply binomials.
- Check the factoring
Multiply the binomial to check it by using the FOIL method: multiply first terms, then outside terms, then inside, then last.
- Rewrite the expression
Rewrite the expression in its simplest form. The example would be written as (x - 3)(x + 4)/(x + 2)(x - 5).
- Find the rational zeros
Rational zeros are the values of the denominator that would cause it to reduce to zero, leaving an undefined ratio. You cannot divide by zero. Because the denominator contains two terms and multiplying any number by zero would yield zero, there are two possible results. In the example problem, the values would be -2 and 5. The higher the degree of a polynomial, the more zeros it has.