1. Algebra 2 9.6 – S OLVING R ATIONAL E QUATIONS

2. O BJECTIVES  Revisit concepts of least common denominators  Solve rational equations  Understand and identify extraneous solutions

3. A N E QUATION WITH O NE S OLUTION  Solve: Main Ideas: Create common denominators, just as we did in 9.5 Once we have common denominators, we can ignore the denominators Solve the equation in the numerator Check your solutions to make sure they work Create common denominators Ignore denominators because they are the same

4. A N E QUATION WITH AN E XTRANEOUS S OLUTION  Solve: Main Ideas: Create common denominators, just as we did in 9.5 Once we have common denominators, we can ignore the denominators Solve the equation in the numerator Check your solutions to make sure they work Although x = 2 appears to be a solution, if you plug it into the original equation, we would have a zero in the denominator. Therefore, this is an extraneous solutions. Create common denominators Distribute

5. E XAMPLES  Solve: 1.2. and

6. A N E QUATION WITH T WO S OLUTIONS  Solve: and Main Ideas: Create common denominators, just as we did in 9.5 Once we have common denominators, we can ignore the denominators Solve the equation in the numerator Check your solutions to make sure they work Create common denominators Distribute Factor Factor the second denominator

7. S OLVING AN E QUATION BY C ROSS M ULTIPLYING  Solve: Main Ideas: Cross multiply and simplify Write in standard form and factor Check your solutions to make sure they work and Although x = 2 and x = 1 appear to be a solutions, if you plug x = 1 into the original equation, we would have a zero in the denominator. Therefore, this is an extraneous solutions. Cross multiply Get terms on same side of equal sign Distribute Factor

8. E XAMPLES  Solve: 3.4. no solution

9. A SSIGNMENT  pgs. 571-572 #24-26, 42-44  Quiz 9.4-9.6 on Wednesday, May 15 th  Chapter 9 Test on Friday, May 17 th