 # Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 14 Rational Expressions.

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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 14 Rational Expressions

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 14.5 Solving Equations Containing Rational Expressions

Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Equations Containing Radical Expressions To solve equations containing rational expressions, clear the fractions by multiplying both sides of the equation by the LCD of all the fractions. Then solve the simplified equation as in previous sections.

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solve: Multiply both sides by the LCD, 6x. Apply the distributive property. Simplify. Continued Example

Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. True To check, we replace x with 10 in the original equation. Check: continued

Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. To Solve an Equation Containing Rational Expressions Step 1:Multiply both sides of the equation by the LCD of all rational expressions in the equation. Step 2:Remove any grouping symbols and solve the resulting equation. Step 3:Check the solution in the original equation.

Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solve the following rational equation. continued Example

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. True Check: Substitute the value for x into the original equation. The solution is continued

Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solve: continued Example

Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Check: Substitute the value for x into the original equation. True The solution is x = 3. continued

Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solve the following rational equation. continued Example

Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Check: Substitute the value for x into the original equation. Notice that 3 makes a denominator 0 in the original equation. Therefore, 3 is not a solution and the equation has no solution. continued

Martin-Gay, Developmental Mathematics, 2e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Helpful Hint As we can see from the previous example, it is important to check the proposed solution(s) in the original equation.