1.  Chapter 8 – Rational Expressions and Equations 8.6 – Solving Rational Equations and Inequalities

2.  Today we will be learning how to:  Solve rational equations  Solve rational inequalities

3. 8.6 – Solving Rational Equations and Inequalities  Rational Equation – any equation that contains one or more rational expressions  15 + x = 6 x

4. 8.6 – Solving Rational Equations and Inequalities  Rational equations are easier to solve if the fractions are eliminated  You can eliminate the fractions by multiplying each side of the equation by the least common denominator (LCD)  REMEMBER: When you multiply each side by the LCD, EACH TERM on EACH SIDE must be multiplied

5. 8.6 – Solving Rational Equations and Inequalities  Example 1  Solve 5/24 + 2/(3 – x) = 1/4

6. 8.6 – Solving Rational Equations and Inequalities  When solving a rational equation, any possible solution that results in a zero in the denominator MUST be excluded from your list of solutions

7. 8.6 – Solving Rational Equations and Inequalities  Example 2  Solve (p 2 – p + 1)/(p + 1) = (p 2 – 7)/(p 2 – 1) + p

8. 8.6 – Solving Rational Equations and Inequalities  Example 3  Tim an Ashley mow lawns together. Tim working alone could complete a particular job in 4.5 hours, and Ashley could complete it alone in 3.7 hours. How long does it take to complete the job when they work together?

9. 8.6 – Solving Rational Equations and Inequalities  Example 4  Janine swims for 5 hours in a stream that has a current of 1 mile per hour. She leaves her dock, swims upstream for 2 miles and then swims back to her dock. What is her swimming speed in still water?  d = rt or d/r = t

10. 8.6 – Solving Rational Equations and Inequalities  Rational Inequalities – Inequalities that contain one or more rational expressions  To solve rational expressions, complete the following steps:  State the excluded values  Solve the related equation  Use the values determined in steps 1 and 2 to divide a number line into intervals. Test a value in each interval to determine which intervals contain values that satisfy the original inequality

11. 8.6 – Solving Rational Equations and Inequalities  Example 5  Solve 1/3s + 2/9s < 2/3

12. 8.6 – Solving Rational Equations and Inequalities HOMEWORK Page 484 #11 – 21 odd, 22 – 23 all, #25 – 29 odd, 30