171S3.4 Solving Rational Equations & Radical Equations. February 23, Some Media for this Section
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1 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 Some Media for this Section 1. Solving Rational Equations 1 solving simple equations with algebraic fractions Solving Rational Equations 2 solving more complex equations with algebraic fractions Solving Radical Equations solving equations with square roots. Watch this very good (9 min) video on solving rational equations. Graphs of Rational Functions: Part 1; Graphs of Rational Functions: Part Solving Rational Equations and Radical Equations Solve rational equations. Solve radical equations. Solution: Multiply both sides by the LCD 6. 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. 1
2 (continued) The possible solution is 5. Solution: Multiply both sides by the LCD x 3. The solution is 5. (continued) The possible solutions are 3 and 3. Check x = 3: Check x = 3: 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 a n = b n is true. Not Defined The number 3 checks, so it is a solution. Division by 0 is not defined, so 3 is not a solution. 2
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. Solve Solution Check x = 5: 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. The solution is 5. Solution: First, isolate the radical on one side. (continued) The possible solutions are 9 and 2. Check x = 9. Check x = 2. FALSE Since 9 checks but 2 does not, the only solution is 9. 3
4 Solution: (continued) We check the possible solution, 4, on a graphing calculator. Graph the two functions and find point of intersection. Since y 1 = y 2 when x = 4, the number 4 checks. It is the solution. 282/6. Solve Graph the two functions and find point of intersection. Follow the screens across from left to right in row one and in row two. See instructions for this method at intersect.htm 4
5 282/14. Solve 282/18. Solve 282/22. Solve 5
6 282/32. Solve 282/36. Solve 283/76. Solve 283/58. Solve 6
7 283/78. Solve m 1/2 = 7 283/82. Solve 283/84. Solve 7
February 27, S3.4q Solving Rational Equations and Radical Equations TRUE. The solution is 5.
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
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