Simplifying Rational Expressions

After studying this lesson, you will be able to:

• Simplify rational expressions.

A rational expression is a fraction that contains at least one variable.

There are basically 2 steps to simplify a rational expression :

1. Factor the numerator and the denominator

2. Cancel

** Only a binomial can cancel a binomial.

** Never cancel part of a binomial or part of a trinomial. You can cancel part of a monomial.

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I. Simplifying Monomials:

Example 1

This is actually a review. We already know how to simplify monomials. First, cancel or reduce the coefficients. 10 and 8 reduces to 5 and 4 Second, divide the variables. Remember to subtract exponents when dividing. This is the simplified expression.

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Example 2

This is actually a review. We already know how to simplify monomials. First, cancel or reduce the coefficients. 24 and 8 reduces to 3 and 1 Second, divide the variables. Remember to subtract exponents when dividing. This is the simplified expression.

II. Dividing by a Monomial

Example 3

Divide each term in the numerator by 2x   This is the simplified expression.

Example 4

Divide each term in the numerator by 2x   This is the simplified expression.

Example 5

Divide each term in the numerator by 6 This is the simplified expression.

III. Dividing by a Binomial or Trinomial

Example 6

Factor the numerator and the denominator.   Cancel the binomials that are identical. (x+1) cancels (x+1)   Do not cancel the remaining x's... never cancel part of a binomial

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Example 7

Factor the numerator and the denominator.   Factor Completely   Cancel the 3's and cancel (m+4)

Example 8

Factor the numerator and the denominator.   Factor out 2 in the numerator and -1 in the denominator   Factor Completely   Cancel out ( x - y )