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10. 7 Solving Rational Equations. Standard: ALG. 15.0. Main Idea & Vocabulary. Today, we will solve rational equations. Like working with fractions, be sure to find a common denominator. Rational equation : an equation with one or more rational expression.

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Main idea vocabulary
Main Idea & Vocabulary

  • Today, we will solve rational equations. Like working with fractions, be sure to find a common denominator.

  • Rational equation: an equation with one or more rational expression.

    • Like a proportion, you can use the Cross Product Property

  • Extraneous 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 products
Ex. 1 Solving by Cross Products

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

    1) cross multiply

    2) Solve for variable using inverse operations (Ch. 2)



Ex 2 solving by lcd
Ex. 2 Solving by LCD

  • Step 1: Find the LCD

  • Step 2: Multiply each fraction by the LCD to cancel the denominator

  • Step 3: Simplify and solve



Ex 3 extraneous solutions
Ex. 3 Extraneous Solutions

  • Check your answer! Some solutions may not work for the original equation, these are extraneous solutions (excluded values).



Review

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

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

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

Are excluded values always extraneous solutions?

Review


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