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?