Chapter 7 Section 6. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Equations with Rational Expressions Distinguish between.

Slides:



Advertisements
Similar presentations
Chapter 7 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Advertisements

The Fundamental Property of Rational Expressions
Warm Up Simplify each expression. Factor the expression.
Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,
Table of Contents First, find the least common denominator (LCD) of all fractions present. Linear Equations With Fractions: Solving algebraically Example:
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
CHAPTER 4 Fraction Notation: Addition, Subtraction, and Mixed Numerals Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4.1Least Common.
Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying and Dividing Rational Expressions Multiply rational.
Chapter 7 Section 1. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 The Fundamental Property of Rational Expressions Find the numerical.
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 1 Section 2.2 The Multiplication Property of Equality Copyright © 2013, 2009, 2006 Pearson Education,
Chapter 7 Section 4. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.
Other Types of Equations
Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for.
Chapter 6 Section 6 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Equations with Rational Expressions Distinguish between.
Chapter 6 Section 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 The Fundamental Property of Rational Expressions Find the numerical.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Equations and Inequalities Chapter 2.
Mathematics for Business and Economics - I
Section 1Chapter 2. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Linear Equations in One Variable Distinguish between expressions.
Chapter 2 Section 1 Copyright © 2011 Pearson Education, Inc.
Chapter 4 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 7 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 7 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 6 Section 4 Addition and Subtraction of Rational Expressions.
Chapter 6 Section 4 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.
CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 12 Rational Expressions.
Copyright © 2013 Pearson Education, Inc. Section 2.2 Linear Equations.
Solving Rational Equations On to Section 2.8a. Solving Rational Equations Rational Equation – an equation involving rational expressions or fractions…can.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations.
11-9 Rational Equations and Functions Algebra 1 Glencoe McGraw-HillLinda Stamper.
Chapter 2 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Solving Equations with Rational Expressions Distinguish between operations with rational expressions and equations with terms that are rational expressions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.3 Further Solving Linear Equations.
Solution Because no variable appears in the denominator, no restrictions exist. The LCM of 5, 2, and 4 is 20, so we multiply both sides by 20: Example.
Chapter 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Solving Linear.
§ 6.6 Rational Equations. Blitzer, Intermediate Algebra, 5e – Slide #2 Section 6.6 Solving a Rational Equation A rational equation, also called a fractional.
Chapter 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Solving Linear.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 14 Rational Expressions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.8 Solving Equations Containing Fractions.
Copyright © Cengage Learning. All rights reserved. Rational Expressions and Equations; Ratio and Proportion 6.
Chapter 4 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Systems of Linear Equations by Elimination Solve linear.
Chapter 6 Section 6 Solving Rational Equations. A rational equation is one that contains one or more rational (fractional) expressions. Solving Rational.
Solving Rational Equations
Chapter 1 Section 8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 1 Simplifying Expressions Simplify expressions. Identify terms and.
Solving a System of Equations in Two Variables By Substitution Chapter 8.2.
Martin-Gay, Beginning Algebra, 5ed Solve the following rational equation.EXAMPLE Because no variable appears in the denominator, no restrictions.
Chapter 2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1 Solving Linear Equations and Inequalities.
1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Linear Equations in One Variable Distinguish between expressions and equations.
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 6.6 Rational Equations Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.
Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.
Chapter 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-1 Rational Expressions and Equations.
Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.
Copyright © 2013, 2009, 2006 Pearson Education, Inc.
Rational Expressions and Equations
Chapter 2 Section 3.
Solving Rational Equations and Radical Equations
Solving Equations Containing Fractions
Objective Solve equations in one variable that contain more than one operation.
Chapter 2 Section 1.
Copyright © Cengage Learning. All rights reserved.
Introduction Solving inequalities is similar to solving equations. To find the solution to an inequality, use methods similar to those used in solving.
Chapter 2 Section 1.
Rational Expressions and Equations
Objective Solve equations in one variable that contain more than one operation.
Adding and Subtracting Rational Expressions
Chapter 2 Section 3.
Solving Equations Containing Fractions
Solving Equations Containing Rational Expressions § 6.5 Solving Equations Containing Rational Expressions.
Linear Equations and Applications
Presentation transcript:

Chapter 7 Section 6

Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solving Equations with Rational Expressions Distinguish between operations with rational expressions and equations with terms that are rational expressions. Solve equations with rational expressions. Solve a formula for a specified variable

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Distinguish between operations with rational expressions and equations with terms that are rational expressions. Slide 7.6-3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Distinguish between operations with rational expressions and equations with terms that are rational expressions. Before solving equations with rational expressions, you must understand the difference between sums and differences of terms with rational coefficients, or rational expressions, and equations with terms that are rational expressions. Sums and differences are expressions to simplify. Equations are solved. Uses of the LCD When adding or subtracting rational expressions, keep the LCD throughout the simplification. When solving an equation, multiply each side by the LCD so the denominators are eliminated. Slide 7.6-4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Identify each of the following as an expression or an equation. Then simplify the expression or solve the equation. equation expression Slide EXAMPLE 1 Distinguishing between Expressions and Equations

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Solve equations with rational expressions. Slide 7.6-6

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve equations with rational expressions. When an equation involves fractions, we use the multiplication property of equality to clear the fractions. Choose as multiplier the LCD of all denominators in the fractions of the equation. Recall from Section 7.1 that the denominator of a rational expression cannot equal 0, since division by 0 is undefined. Therefore, when solving an equation with rational expressions that have variables in the denominator, the solution cannot be a number that makes the denominator equal 0. Slide 7.6-7

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the solution. Solution: Check: The use of the LCD here is different from its use in Section 7.5. Here, we use the multiplication property of equality to multiply each side of an equation by the LCD. Earlier, we used the fundamental property to multiply a fraction by another fraction that had the LCD as both its numerator and denominator. Slide EXAMPLE 2 Solving an Equation with Rational Expressions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. While it is always a good idea to check solutions to guard against arithmetic and algebraic errors, it is essential to check proposed solutions when variables appear in denominators in the original equation. Solving an Equation with Rational Expressions Step 1: Multiply each side of the equation by the LCD to clear the equation of fractions. Be sure to distribute to every term on both sides. Step 2: Solve the resulting equation. Step 3: Check each proposed solution by substituting it into the original equation. Reject any that cause a denominator to equal 0. Slide Solve equations with rational expressions. (cont’d)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. When the equatioin is solved, − 1 is a proposed solution. However, since x = − 1 leads to a 0 denominator in the original equation, the solution set is Ø. Slide EXAMPLE 3 Solving an Equation with Rational Expressions Ѳ

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. The solution set is {4}. Slide EXAMPLE 4 Solving an Equation with Rational Expressions Ѳ

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Solve, and check the proposed solution. Since 0 does not make any denominators equal 0, the solution set is {0}. Slide EXAMPLE 5 Solving an Equation with Rational Expressions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the proposed solution (s). Solution: The solution set is {−4, −1}. or Slide EXAMPLE 6 Solving an Equation with Rational Expressions Ѳ

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve, and check the proposed solution. Solution: The solution set is {60}. Slide EXAMPLE 7 Solving an Equation with Rational Expressions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Solve a formula for a specified variable. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve each formula for the specified variable. Solution: Remember to treat the variable for which you are solving as if it were the only variable, and all others as if they were contants. Slide EXAMPLE 8 Solving for a Specified Variable

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solve the following formula for z. Solution: When solving an equation for a specified variable, be sure that the specified variable appears alone on only one side of the equals symbol in the final equation. Slide EXAMPLE 9 Solving for a Specified Variable

Copyright © 2012, 2008, 2004 Pearson Education, Inc. HL# 7.6 Book Beginning Algebra Page 463# 19,21,24,26,31,32,38,41,47,49,54,56. Page 464# 63,64,69,73,75,86,90,94.