1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Solve a rational equation or inequality by using algebra, a table, or a graph. Solve problems by using a rational equation or inequality. 8.5 Solving Rational Equations and Inequalities

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms extraneous solution rational equation rational inequality 8.5 Solving Rational Equations and Inequalities

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve rational equations. 8.5 Solving Rational Equations and Inequalities x x + 2 1 x = x 2 = x + 2 x 2 – x – 2 = 0 (x – 2)(x + 1) = 0 x = 2 or x = –1

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve rational inequalities. 8.5 Solving Rational Equations and Inequalities Case 1 (x + 2 > 0)Case 2 (x + 2 < 0) 1 –1.5 x > –2 and x > –1.5 x > –1.5 1 > 2x + 4; x < –1.5 x < –2 and x < –1.5 x < –2or 1 x + 2 < 2

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve rational inequalities. 8.5 Solving Rational Equations and Inequalities another method: Find where the graph of is below the graph of y = 2. 1 x + 2 y = 1 x + 2 < 2 TOC