Chapter 11.2 Notes: Simplify Rational Expressions Goal: You will simplify rational expressions.

A rational expression is an expression that can be written as a ratio of two polynomials where the denominator is not 0. i.e. A rational expression is undefined when the denominator is 0. A number that makes a rational expression undefined is called an excluded value.

Simplifying a Rational Expression To simplify a rational expression, you must ALWAYS factor the numerator and denominator, if necessary, and then divide out any common factors. A rational expression is in simplest form if the numerator and denominator have no factors in common other than 1. i.e.

Ex.1: Simplify the rational expression, if possible. a. c. b. d.

Ex.2: Simplify the rational expression, if possible. a. b. c. d. Ex.3: Simplify to lowest terms.

Ex.4: Simplify Ex.5: Simplify the rational expression. a. b. c.

Ex.6: Simplify the rational expression. a. b. c. d.

Ex.7: Simplify the rational expression. a. c. b. d.