3.4 Solving Rational Equations and Radical Equations Solve rational equations. Solve radical equations. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Rational Equations Equations containing rational expressions are called rational equations. Solving such equations requires multiplying both sides by the least common denominator (LCD) to clear the equation of fractions. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Solve: Solution: Multiply both sides by the LCD 6. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example (continued) The possible solution is 5. Check: TRUE The solution is 5. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Solve: Solution: Multiply both sides by the LCD x  3. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example (continued) The possible solutions are –3 and 3. Check x = –3: Check x = 3: TRUE Not Defined The number 3 checks, so it is a solution. Division by 0 is not defined, so 3 is not a solution. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Radical Equations A radical equation is an equation in which variables appear in one or more radicands. For example: The Principle of Powers For any positive integer n: If a = b is true, then an = bn is true. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Solving Radical Equations To solve a radical equation we must first isolate the radical on one side of the equation. Then apply the Principle of Powers. When a radical equation has two radical terms on one side, we isolate one of them and then use the principle of powers. If, after doing so, a radical terms remains, we repeat these steps. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Solve Solution Check x = 5: TRUE The solution is 5. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example Solve: Solution: First, isolate the radical on one side. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Example (continued) The possible solutions are 9 and 2. Check x = 9. Check x = 2. TRUE FALSE Since 9 checks but 2 does not, the only solution is 9. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley