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10. 7 Solving Rational Equations

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10. 7 Solving Rational Equations

Standard: ALG. 15.0

- 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!

- To solve one with two rational expressions, solve like a proportion:
1) cross multiply

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

- Step 1: Find the LCD
- Step 2: Multiply each fraction by the LCD to cancel the denominator
- Step 3: Simplify and solve

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

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?