Simplifying Rational Expressions

Simplifying and performing operations on rational expression can be very challenging for my students, but reinforcing the connection to numeric fractions seems to make it easier.   I introduce the warm-up WS Fraction Practice as a "throw back" assignment because it's math that my students learned in elementary school.  This warm up is designed to remind students of the procedures for  simplifying and operating on fractions.

After my students have spent time reviewing how to work with fractions, I introduce the concept of an algebraic fraction.  Students take a few notes on vocabulary related to rational expressions, including the following terms:

• a rational expression is a ratio of two polynomial expressions in which the denominator has degree one or more
• the domain of a rational expression is restricted to prevent division by zero
• to simplify a rational expression means to divide both the top and bottom of the expression by all common factors (which is often called "canceling" common factors)

When these concepts have been clarified, students are ready to work with their table group to complete WS Intro to Simplifying Rational Expressions.  This worksheet walks students through identification of the domain of rational expressions and simplification of rational expressions.

As an engaging way to continue practicing simplifying rational expressions, I ask my students to work in pairs to complete Row Game Rational Expressions.  In a row game, two people work on the same worksheet, which is divided into two columns.  The answer to the first problem in column A is the same as the answer to the first problem in column B, even though the problems look very different.  Likewise the answers to the second and third problems are the same in both columns.  I like to use row games for practice, because it promotes dialog about math [MP3].  Students work out their own problem and often spend time convincing their partner about the validity of their method.

For additional practice with simplifying rational expressions and identifying the domain, I assign students WS Simplifying Rational Expressions for homework.  I anticipate that this practice will take them about 30 minutes to complete.  I make solutions to this worksheet available to students through Edmodo.