Lesson 7EWe All Scream for Ice CreamPractice Understanding

Learning Focus

Solve equations that contain rational expressions.

What real-life situations can be modeled with rational functions?

Open Up the Math: Launch, Explore, Discuss

4.

This story and the problem it represents provide an opportunity to model a situation that requires a rational equation. Rational equations can take many forms, but they are solved using principles we have worked with before. Try applying some of the strategies for working with rational expressions that we have used in this unit to solve these equations.

8.

Try to solve this challenging equation:

Takeaways

Useful strategies for solving rational equations:

Extraneous solution:

Lesson Summary

In this lesson, we learned several strategies for solving rational equations. We found that it is often useful to combine two fractions into one expression or to multiply both sides of the equation by the common denominator of the fractions. Solving rational equations sometimes produces an extraneous solution that makes the denominator of one of the rational expressions in the original equation equal to zero and is therefore not an actual solution to the equation.

Retrieval

1.

The side lengths of right triangle are , , and . If is the numerator of in the triangle, what is the trigonometric ratio for ?