This is the third of three lessons about solving rational equations. Two equations are equivalent if they have the same solution set. The purpose of this lesson is for students to practice solving rational equations strategically and understand how certain steps in the solving process can lead to equations that are not equivalent to the initial equation. If a step in the solving process results in a new equation that has more solutions than the initial equation, people sometimes call these additional solutions extraneous solutions. One step that often results in an equation that is not equivalent is when each side of an equation is multiplied by an expression that can take on the value of 0, which could in turn make two previously unequal (or undefined) sides equal. In particular, this lesson gives students the chance to use precise language to explain how a solution is not always a solution due to multiplication by 0 (MP6).
The first few activities help develop students’ understanding for how these extra, or extraneous, solutions can arise when solving rational equations. The last activity of the lesson provides practice for solving rational equations. Students first identify which equations they consider most and least difficult, and then select three to solve with a partner and check for possible extraneous solutions.
Lesson overview
 22.1 Warmup: Notice and Wonder: Thoughtful Multiplication (5 minutes)

22.2 Activity: Rational Solving (15 minutes)
 Includes "Are you Ready for More?" extension problem
 22.3 Activity: More Rational Solving (15 minutes)
 Lesson Synthesis
 22.4 Cooldown: Find Rational Solutions (5 minutes)
Learning goals:
 Determine whether there are extraneous solutions to a rational equation.
 Explain (orally and in writing) how extraneous solutions can arise when solving rational equations.
Learning goals (student facing):
 Let’s think about how to solve rational equations strategically.
Learning targets (student facing):
 I know how to check for extraneous solutions to rational equations.
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