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Solving Rational Equations and Radical Equations

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Presentation on theme: "Solving Rational Equations and Radical Equations"— Presentation transcript:

1 Solving Rational Equations and Radical Equations
Section 3.4 Solving Rational Equations and Radical Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

2 Objectives Solve rational equations. Solve radical equations.

3 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.

4 Example Solve: Multiply both sides by the LCD 6.

5 Example (continued) The possible solution is 5. Check: TRUE
The solution is 5.

6 Example Solve: Multiply both sides by the LCD x  3.

7 Example (continued) The possible solutions are –3 and 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.

8 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.

9 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.

10 Example Solve Check x = 5: TRUE The solution is 5.

11 Example Solve: First, isolate the radical on one side.

12 Example (continued) The possible solutions are 9 and 2. Check x = 9.
TRUE FALSE Since 9 checks but 2 does not, the only solution is 9.

13 Example Solve:

14 Example (continued) We check the possible solution, 4, on a graphing calculator. Since y1= y2 when x = 4, the number 4 checks. It is the solution.


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