Q:

# How do you find the vertical asymptotes of a rational function?

A:

### Quick Answer

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.

Continue Reading

## Keep Learning

Credit: Jeffrey Coolidge The Image Bank Getty Images

### Full Answer

1. 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.

2. Check the factoring

Multiply the binomial to check it by using the FOIL method: multiply first terms, then outside terms, then inside, then last.

3. Rewrite the expression

Rewrite the expression in its simplest form. The example would be written as (x - 3)(x + 4)/(x + 2)(x - 5).

4. 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.

Learn more about Algebra
Sources:

## Related Questions

• A: Similar terms in algebra, sometimes referred to as like terms, are terms that contain the same variables raised to the same power. In algebraic expressions... Full Answer >
Filed Under:
• A: Monomials and binomials can be subtracted from each other by subtracting coefficients of terms with the same degree and leaving the variable untouched. Mon... Full Answer >
Filed Under:
• A: To solve multi-step equations in algebra, you need to collect like terms, simplify the expressions and follow the order of operations to isolate the variab... Full Answer >
Filed Under:
• A: One simplifies polynomial expressions by adding and subtracting like terms. To find like terms, one needs to compare the variable parts of the polynomial's... Full Answer >
Filed Under:
PEOPLE SEARCH FOR