8.5 Solving Rational Equations

Steps to solve Rational Equations Find common denominator Find restrictions Cross out all denominators Solve for x Check for restricted values of x

Example 1 3 2 LCD:

3 2 Example 2 LCD:

3 8 16 Example 3 LCD:

Example 4 LCD:

8-5 : Solving Rational Equations Example 5 4/6/2019 12:28 AM 8-5 : Solving Rational Equations

Therefore, the equation has no solution. Example 6 (x – 2) (x – 2) 5x x – 2 3x + 4 = 5x = 3x + 4 2x = 4 No Solution x = 2 The solution x = 2 is extraneous because it makes the denominators of the original equation equal to 0. Therefore, the equation has no solution. 4/6/2019 12:28 AM 8-5 : Solving Rational Equations

Example 7 LCD:

Example 8 LCD:

Example 9

Example 10

Example 11 LCD:

Example 12

Example 13