2. Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:

3. To solve a rational equation: 1) Find the LCD of all rational expressions in the equation. 2) Multiply both sides of the equation by the LCD. 3) Solve the resulting equation.

4. Example 1 First determine any restrictions on the variable. These are values of x for which any denominator is zero. Solve: In this case, x cannot be zero.

5. Determine the LCD Multiply both sides of the equation by the LCD

7. These solutions must be compared with the restriction on x found at the beginning of the problem, x ≠ 0. Since neither value is zero, we have the solution.

8. Example 2 Determine any restrictions on the variable. Solve:

9. Determine the LCD Multiply both sides of the equation by the LCD. This is the same as multiplying every term by the LCD.

12. Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 4,2. Since the solution does not match either restriction, we have the solution.

13. Example 3 Determine any restrictions on the variable. Solve:

14. Determine the LCD Multiply every term by the LCD.

16. Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 5,0. Since in this case the result is one of the restricted values, it cannot be a solution to the equation. The answer is written as …