# Lesson 21

Rational Equations (Part 2)

### Lesson Narrative

This is the second of three lessons highlighting solving rational equations. In this lesson, students write and solve equations involving rational expressions with different denominators and interpret the equations and solutions in context (MP2). Building on the reasoning established in the previous lesson, students continue to use strategic multiplication to change the structure of the equation to linear, which they then solve (MP7). In the next lesson, students address the extraneous solutions that can arise when solving rational equations.

The warm-up invites students to recall what they know about equivalent fractions and to apply their understanding to solve equations involving simple rational expressions with unlike denominators. Then, students return to the relationship between distance, rate, and time, and create expressions for the time it takes a boat to travel a certain distance upstream and a certain distance downstream in order to calculate the rate of flow of the water in the river. In the last activity, students work with the formula for the total resistance of circuits in parallel.

### Learning Goals

Teacher Facing

• Create a simple equation involving two rational expressions to model a situation and use the model to answer questions.
• Use strategic multiplication to solve equations that have rational expressions on both sides.

### Student Facing

• Let’s write and solve some more rational equations.

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)

### Student Facing

• I can write and solve equations with simple rational expressions on each side.