10. 7 Solving Rational Equations10. 7 Solving Rational Equations

Standard: ALG. 15.0

Main Idea & VocabularyMain Idea & Vocabulary• Today, we will solve rational equations. Like working Today, we will solve rational equations. Like working

with fractions, be sure to find a common with fractions, be sure to find a common denominator.denominator.

• Rational equationRational equation: an equation with one or more rational expression.– Like a proportion, you can use the Cross Product Property

• Extraneous solutionExtraneous solution: a solution to a resulting equation (after finding the LCD) that is NOT a solution to the original equation.

• (A.K.A excluded value when O on the bottom is undefined)– Check your answers!

Ex. 1 Solving by Cross ProductsEx. 1 Solving by Cross Products

• To solve one with two rational expressions, solve like a proportion:

1) cross multiply2) Solve for variable using

inverse operations (Ch. 2)

PracticePractice

Ex. 2 Solving by LCDEx. 2 Solving by LCD

• Step 1Step 1: Find the LCD: Find the LCD• Step 2Step 2: Multiply : Multiply

each fraction by the each fraction by the LCD to cancel the LCD to cancel the denominatordenominator

• Step 3Step 3: Simplify and : Simplify and solvesolve

PracticePractice

Ex. 3 Extraneous SolutionsEx. 3 Extraneous Solutions• Check your answer! Some solutions may not work for the original

equation, these are extraneous solutions (excluded values).

Practice Practice

ReviewReview

• When can you use cross products to solve a When can you use cross products to solve a rational equation?rational equation?

• What is the purpose of multiplying both sides What is the purpose of multiplying both sides by the LCD?by the LCD?

• How are the extraneous solutions related to How are the extraneous solutions related to the denominators in the equation?the denominators in the equation?

• Are excluded values always extraneous Are excluded values always extraneous solutions?solutions?