1. Rational Expressions and Equations
Chapter 6
Rational Expressions and Equations

2. Chapter Sections
6.1 – The Domains of Rational Functions and Multiplication and Division of Rational Expressions
6.2 – Addition and Subtraction of Rational Expressions
6.3 – Complex Fractions
6.4 – Solving Rational Equations
6.5 – Rational Equations: Applications and Problem Solving
6.6 – Variation
Chapter 1 Outline

3. Solving Rational Equations
§ 6.4
Solving Rational Equations

4. Solve Rational Equations
A rational equation is an equation that contains at least one rational expression.
Examples:

5. Solve Rational Equations
To Solve Rational Equations
Determine the LCD of all rational expressions in the equation.
Multiply both sides of the equation by the LCD. This will result in every term in the equation being multiplied by the LCD. This will eliminate all of the fractions from the equation.
Remove any parentheses and combine like terms on each side of the equation.
Solve the equation using the properties discussed in earlier sections.
Check the solution in the original equation.

6. Solve Rational Equations
Example Solve

7. Check Solutions
When solving a rational equation with a variable in any denominator, you must check the value(s) obtained in the original equation. Since division by 0 is undefined, the value that makes a denominator 0 is not a solution and is called an extraneous solution.

8. Solve Proportions
Proportion
A proportion is an equation of the form
Proportions may also be solved by cross-multiplication as follows:

9. Solve Proportions Examples: Similar Figures
Similar figures are figures whose corresponding angles are equal and whose corresponding sides are in proportion
Examples:

10. Example
Triangles ABC and A’B’C’ are similar figures. Find the length of sides AB and B’C’.
Since a length of the side cannot be a negative number, -5 is not a possible answer. Substituting 6 for x, we see that the length of side B’C’ is 6 and the length of side AB is 6-1 or 5.

11. Solve Problems Involving Rational Functions
Example Consider the function Find all a for which f(a) = 1.