11-9 Rational Equations and Functions Algebra 1 Glencoe McGraw-HillLinda Stamper

Rational equations are equations that contain rational expressions. You can use cross products to solve rational equations but only when both sides of the equation are single fractions. Cross Product Property If two ratios are equal then their cross products are also equal. Because division by zero is undefined, you must check your answers to make sure that any values of a variable that result in a zero denominator are excluded from the final answer.

Solve. Write the problem. Any value for the variable that results in a zero in the denominator, is not a solution. Cross multiply. Distribute.

Example 1 You must use parentheses! Check: Remember that division by zero is undefined, therefore any value that results in making the denominator zero is not a solution. Solve. Example 2

Another method you can use to solve rational equations is to multiply each side of the equation by the LCD of all of the fractions on both sides of the equation. This will eliminate all of the fractions. This method works for any rational equation. Remember: You can use cross products to solve rational equations but only when both sides of the equation are single fractions.

Multiply both sides by the LCD. Distribute the LCD and simplify. Solve. Multiply and solve.

Example 3 Solve. Example 4

Example 3 Solve.

Example 4 Solve.

Recall that to find the roots of a quadratic function, find the values of x when y = 0. The roots of a rational function are found similarly. Rational Functions Write the problem. Set f(x) = 0. Factor. When x = 4 and -3, the numerator becomes zero, so f(x) = 0. Therefore, the roots of the function are 4 and -3. Check: Remember that division by zero is undefined, therefore any value that results in making the denominator zero is not a solution.

Example 5 Solve. Example 6 Check: Remember that division by zero is undefined, therefore any value that results in making the denominator zero is not a solution.

Example 7 Solve. Example 8 Check: Remember that division by zero is undefined, therefore any value that results in making the denominator zero is not a solution. Example 9 Example 10

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