# Equivalent Rational Expressions

### Modeling Riverbeds with Polynomials

Student Outcomes

• Students define rational expressions and write them in equivalent forms.

### New York State Common Core Math Algebra II, Module 1, Lesson 22

Worksheets for Algebra II, Module 1, Lesson 22

Classwork

Opening Exercise On your own or with a partner, write two fractions that are equivalent to 1/3, and use the slips of paper to create visual models to justify your response.

Example

Consider the following rational expression: (2(𝑎−1)−2)/(6(𝑎−1)−3𝑎). Turn to your neighbor, and discuss the following: For what values of 𝑎 is the expression undefined? this section of the river, measured in gallons per minute?

Exercise

Reduce the following rational expressions to lowest terms, and identify the values of the variable(s) that must be excluded to prevent division by zero.

Lesson Summary

• If 𝑎, 𝑏, and 𝑛 are integers with 𝑛 ≠ 0 and 𝑏 ≠ 0, then
na/nb = a/b
• The rule for rational expressions is the same as the rule for integers but requires the domain of the rational expression to be restricted (i.e., no value of the variable that can make the denominator of the original rational expression zero is allowed).

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