1. Example 1: Solving Rational Equations
8-5 LEARNING GOALS
Solve rational equations and inequalities by hand using algebra.
Solve rational equation and inequalities with a graph and table.
A rational equation is an equation that contains one or more rational expressions and a _________ sign.
Solving for x means that you will have x = in for your answer.
Example 1: Solving Rational Equations
Solve the equations. Check your answer.
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2. Example 2: Extraneous Solutions
An ____________ ____________is a solution that is not a solution of the original equation. Always check your solutions by substituting them into the original equation.
Example 2: Extraneous Solutions
Solve each equation, then check. You can also use your calculator to check your answers, too.
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3. Solve the equations, then check.
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4. A. Solve = 3 by using a graph and a table.
Example 5: Using Graphs and Tables to Solve Rational Equations and Inequalities x
x – 6
A. Solve = 3 by using a graph and a table.
Step 1: Plug in left side to Y1 and right side to Y2
Step 2: Find where the two functions cross (check with table) x
x – 6
B. Solve ≤ 3 by using a graph and a table.
Step 1: Plug in left side to Y1 and right side to Y2
Step 2: Find where the two functions cross determine which x values produce y values less than or equal to 3.
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