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Solving Equations with Rational Expressions

Learn how to distinguish between operations with rational expressions and equations with terms that are rational expressions. Solve equations with rational expressions and solve a formula for a specified variable.

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Solving Equations with Rational Expressions

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  1. Chapter 6 Section 6

  2. 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. 6.6 2 3

  3. Objective 1 Distinguish between rational expressions and equations Slide 6.6-3

  4. Distinguish between expressionsand equations Uses of the LCD • When adding or subtracting rational expressions, find the LCD, then add numerators • When simplifying a complex fraction, multiply numerator and denominator by the LCD • When solving an equation, multiply each side by the LCD so the denominators are eliminated. WOW the LCD is useful! Slide 6.6-4

  5. Identify each of the following as an expression or an equation. Then simplify the expression or solve the equation. CLASSROOM EXAMPLE 1 Distinguishing between Expressions and Equations Solution: equation expression Slide 6.6-5

  6. Objective 2 Solve equations with rational expressions. Slide 6.6-6

  7. Solve equations with rational expressions When an equation involves fractions • use the multiplication property of equality to clear the fractions • choose as multiplier the LCD of all denominators in the fractions of the equation Please recall: The 11th Commandment Thou shall not… divide by zero 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 6.6-7

  8. Solve, and check the solution. CLASSROOM EXAMPLE 2 Solving an Equation with Rational Expressions Solution: Check: Multiply every term of the equation by the LCD Slide 6.6-8

  9. Solving an Equation with Rational Expressions Step 1:Multiply each side of the equation by the LCDto clear the equation of fractions. Be sure to distribute to every term on both sides. Step 2:Solvethe resulting equation. Step 3:Checkeach proposed solution by substituting it into the original equation. Reject any solutions that cause a denominator to equal 0. Slide 6.6-9

  10. Solve, and check the proposed solution. CLASSROOM EXAMPLE 3 Solving an Equation with Rational Expressions Solution: Reject this solution. WHY?? How do you recognize equations that could possibly have restrictions? Slide 6.6-10

  11. Solve, and check the proposed solution. CLASSROOM EXAMPLE 4 Solving an Equation with Rational Expressions Solution: It works! The solution set is {4}. Slide 6.6-11

  12. Solve, and check the proposed solution. CLASSROOM EXAMPLE 5 Solving an Equation with Rational Expressions Solution: Does it work?? The solution set is {0}. Slide 6.6-12

  13. Solve, and check the proposed solution (s). CLASSROOM EXAMPLE 6 Solving an Equation with Rational Expressions Solution: or The solution set is {−4, −1}. Slide 6.6-13

  14. Solve, and check the proposed solution. CLASSROOM EXAMPLE 7 Solving an Equation with Rational Expressions Solution: The solution set is {60}. Slide 6.6-14

  15. Objective 3 Solve a formula for a specified variable. Slide 6.6-15

  16. CLASSROOM EXAMPLE 9 Solving for a Specified Variable Solve the following formula for z. Solution: Fun! Slide 6.6-17

  17. Solve each formula for the specified variable. CLASSROOM EXAMPLE 8 You Try It 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 6.6-16

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