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Chapter 7 Rational Expressions and Equations

Chapter 7 Rational Expressions and Equations. Section 7 Rational Equations. Section 7.7 Objectives. 1 Solve Equations Containing Rational Expressions 2 Solve for a Variable in a Rational Equation. Example: Solve for x. x  0. Solving Equations.

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Chapter 7 Rational Expressions and Equations

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  1. Chapter 7 Rational Expressions and Equations Section 7 Rational Equations

  2. Section 7.7 Objectives 1 Solve Equations Containing Rational Expressions 2 Solve for a Variable in a Rational Equation

  3. Example: Solve for x. x  0 Solving Equations Arational equation is an equation that contains a rational expression. Multiply each term by the LCD 6x. Simplify. Subtract 2 from both sides. Divide both sides by 5.  Check: The solution set is {2}.

  4. Solving Equations Steps to Solve a Rational Equation Step 1: Determine the values(s) of the variable that result in an undefined rational expression in the rational equation. Step 2: Determine the least common denominator (LCD) of all the denominators. Step 3: Multiply both sides of the equation by the LCD, and simplify the expression on each side of the equation. Step 4: Solve the resulting equation. Step 5: Verify your solution using the original equation.

  5. y – 5, y  Solving Equations Example: Solve: Multiply each term by the LCD (y + 5)(3y – 2). Simplify. Distribute to remove parentheses. Add 6 to both sides. Continued.

  6. The solution set is Solving Equations Example continued: Subtract 3y from both sides. Divide both sides by 6 and simplify. Check: 

  7. Extraneous Solution An extraneous solution is a solution that is obtained through the solving process that does not satisfy the original equation.

  8. Solving Equations with No Solutions Example: Solve: a 6 Multiply each term by (a – 6). Simplify. Distribute. Add 5a to both sides. Add 10 to both sides. Continued.

  9. Solving Equations with No Solutions Example continued: Divide both sides by 7. Extraneous solution a = 6 is not in the domain of the variable a, so there is no solution to the equation and the solution set is { } or . Check:

  10. Solving for a Variable Example: In the following finance formula, solve for r: Multiply each side by 1 + r. Distribute and simplify. Subtract P from both sides. Divide both sides by P.

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