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171S3.4q Solving Rational Equations and Radical Equations February 27, 2013 MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 3: Quadratic Functions and Equations; Inequalities 3.1 The Complex Numbers 3.2 Quadratic Equations, Functions, Zeros, and Models 3.3 Analyzing Graphs of Quadratic Functions 3.4 Solving Rational Equations and Radical Equations 3.5 Solving Equations and Inequalities with Absolute Value Go to SAS Curriculum Pathways, use Subscriber Login and User name: able7oxygen. Explore rational functions and radical functions by using Quick Launch # 1436 at http://www.sascurriculumpathways.com/ Some Media for this Section 1. Solving Rational Equations 1 solving simple equations with algebraic fractions. http://cfcc.edu/faculty/cmoore/RationalEquations1.wmv 2. Solving Rational Equations 2 solving more complex equations with algebraic fractions. http://cfcc.edu/faculty/cmoore/RationalEquations2.wmv 3. Solving Radical Equations solving equations with square roots. http://cfcc.edu/faculty/cmoore/SquareRootEquations1.wmv Watch this very good (9min) video on solving rational equations. http://www.youtube.com/watch?v=vKakDNh6Q3k Oct 47:58 PM Feb 263:33 PM Example Solve: Solution: Multiply both sides by the LCD 6. 3.4 Solving Rational Equations and Radical Equations • Solve rational equations. • Solve radical equations. Rational Equations Equations containing rational expressions are called rational equations. The possible solution is 5. Solving such equations requires multiplying both sides by the least common denominator (LCD) to clear the equation of fractions. The solution is 5. Oct 47:58 PM TRUE Oct 47:58 PM 1 171S3.4q Solving Rational Equations and Radical Equations February 27, 2013 Example Radical Equations Solve: Solution: Multiply both sides by the LCD x 3. 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 a n = bn is true. The possible solutions are –3 and 3. Check x = –3: Check x = 3: 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. TRUE The number 3 checks, so it is a solution. Not Defined 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. Division by 0 is not defined, so 3 is not a solution. Oct 47:58 PM Oct 47:58 PM Example Solve: Solution: First, isolate the radical on one side. Example Solve Solution Check x = 5: TRUE The solution is 5. The possible solutions are 9 and 2. Check x = 2. Check x = 9. TRUE FALSE Since 9 checks but 2 does not, the only solution is 9. Oct 47:58 PM Oct 47:58 PM 2 171S3.4q Solving Rational Equations and Radical Equations February 27, 2013 Example Solve: Solution: Graph the two functions and find point of intersection. Follow the screens across from left to right in row one and in row two. We check the possible solution, 4, on a graphing calculator. Graph the two functions and find point of intersection. See instructions for this method at http://cfcc.edu/faculty/cmoore/tiintersect.htm Since y1= y2 when x = 4, the number 4 checks. It is the solution. Oct 47:58 PM Oct 48:38 PM Section 3.4 Solving Rational Equations & Radical Equations 281/6. Solve Section 3.4 Solving Rational Equations & Radical Equations 281/16. Solve 281/12. Solve 281/19. Solve Oct 48:39 PM Oct 48:59 PM 3 171S3.4q Solving Rational Equations and Radical Equations February 27, 2013 Section 3.4 Solving Rational Equations & Radical Equations 281/20. Solve 281/24. Solve Feb 262:27 PM Oct 48:59 PM Section 3.4 Solving Rational Equations & Radical Equations 281/27. Solve Section 3.4 Solving Rational Equations & Radical Equations 281/34. Solve 281/28. Solve 281/38. Solve Oct 48:59 PM Oct 48:59 PM 4 171S3.4q Solving Rational Equations and Radical Equations Section 3.4 Solving Rational Equations & Radical Equations 281/48. Solve February 27, 2013 Section 3.4 Solving Rational Equations & Radical Equations 282/77. Solve 281/60. Solve 282/78. Solve Oct 48:59 PM Oct 48:59 PM Section 3.4 Solving Rational Equations & Radical Equations 282/79. Solve Section 3.4 Solving Rational Equations & Radical Equations 282/81. Solve 282/80. Solve 282/84. Solve Oct 48:59 PM Oct 48:59 PM 5 171S3.4q Solving Rational Equations and Radical Equations Feb 2610:04 AM February 27, 2013 Feb 268:37 AM Section 3.4 Solving Rational Equations & Radical Equations 282/86. Solve 282/88. Solve Oct 48:59 PM Feb 262:56 PM 6
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