## Solving Rational Equations

### Johnny WolfeSanta Rosa District Schools

#### Description

You can solve equations containing fractions by using the least common denominator of all the fractions in the equation. Multiplying each side of the equation by the common denominator eliminates the fractions.

#### Objectives

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for "Solving Rational Equations" (see attached file).
- "Solving Rational Equations" Examples (see attached file).
- "Solving Rational Equations" Worksheet (see attached file).
- "Solving Rational Equations" Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for "Solving Rational Equations" Examples (see attached file).
2. Have marking pens (for overhead).
3. Have "Solving Rational Equations" Examples (see attached file) prepared and ready to demonstrate to students.
4. Have enough copies of "Solving Rational Equations" Worksheet (see attached file) for each student.
5. Have enough copies of "Solving Rational Equations" Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving quadratic equations, and factoring. NOTE: This lesson does not address percents, scientific notation, radicals, absolute value or logarithms. This lesson does not address square roots. Also inverse relationship is not address.

1. Describe to students the process we are going to use and why (see # 1 on attached file "Solving Rational Equations" Examples). Answer student questions and comments.

2. Work Example # 2 (see attached file "Solving Rational Equations" Examples). Help students find the LCD and emphasize that each term must be multiplied by the LCD in order to have a balanced equation. Answer student questions and comments.

3. Work Example # 3 (see attached file "Solving Rational Equations" Examples). Point out to students that they must determine any limitations to the domain before they solve the equation. Point out the importance of checking your solutions. Answer student questions and comments.

4. Work Example # 4 (see attached file "Solving Rational Equations" Examples). Answer student questions and comments.

5. Work Example # 5 (see attached file "Solving Rational Equations" Examples). Answer student questions and comments.

6. Work Example # 6 (see attached file "Solving Rational Equations" Examples). Emphasize again the importance of finding the restrictions on the domain before solving the equation. Answer student questions and comments.

7. Work Example # 7 (see attached file "Solving Rational Equations" Examples). Answer student questions and comments.

8. Distribute the "Solving Rational Equations" Worksheet (see attached file).

9. Distribute the "Solving Rational Equations" Checklist (see attached file). Describe what is expected of the student based on the checklist.

10. The student will write their response on the worksheet.

11. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

The student worksheet will be collected and scored according to the "Solving Rational Equations" Checklist (see attached file).

#### Extensions

Give students a triangle with rational expressions for the sides. Then give them the perimeter of the triangle. Have students solve for the variable.