1. 10.6 Solving Rational Equations • Goals: To solve problems involving rational expressions

2. Rational Equation An equation containing one or more rational expressions

3. Steps to solve Rational Equations • Find the LCD • Multiply every term on both sides of the equation by the LCD over 1(objective is to cancel out the denominators) • Solve for the variable a. If it is a linear equation get variables on one side and constants on the other b. If it is a quadratric set your equation = 0 and factor.

4. Extraneous Solutions • When both sides of the equation are mult by a variable, the equation is transformed into a new equation and may have an extra solution. • Check each solution in the original rational equation • Make sure that your answer does not make the denominator 0

5. Solving Rational Equations Multiply both sides of the equation by the LCM of the denominators. Least Common Multiple: Each factor raised to the greatest exponent.

6. Solve for x: LCM =

7. •(x + 1)(x) (x + 1)(x)• Solve for x: LCM = (x + 1)(x)

8. 2x• •2x Solve for x: LCM = 2x

9. Solve for x: x• • x

10. Solve for x: -2 is an extraneous solution.

11. Solve for x: -2 is an extraneous solution.

12. Cross productsShort cut: extraneous solution?

13. Cross products:

14. Cross products:

15. Cross products:

16. Assignment:Page 453# (2-24) even