1. 9.6 Solving Rational Equations
p.569

2. Short Cut!
When there is only fraction on each side of the equal sign, just cross-multiply as if you are solving a proportion.

3. Example: Solve.
Check your solutions!

4. Example: Solve.
Check your solutions!

5. Hint for solving:
One method to solve a rational equation is to multiply everything through by the LCD.
This will get rid of all the fractions!
Beware of extraneous solutions!

6. Multiply each fraction through by the LCD
Example: Solve.
LCD: 2x
Multiply each fraction through by the LCD
Check your solution!

7. Solve.
LCD: ?
LCD: (x+1) ?
Check your solution!
No Solution!

8. Solve.
Factor 1st!
LCD: (x+2)(x-2)
Check your solutions!

9. Here is another example that we will do together:

10. Step 1: Find the LCD This denominator can be factored into 3(x-2)
Hint: Factor the denominator
This denominator can be factored into 3(x-2)
But you need at least a 6 from the other denominator
Therefore….

11. Step 2: Multiply both sides of equation by LCD
Step 2: Multiply both sides of equation by LCD. This eliminates the fractions when you cancel the matching factors.

12. Step 3: Solve for x

13. Since there are two answers, there need to be two checks.
Let x =

14. Check #2:
Let x = 2
When you check the number 2, you get a zero in the denominator. This means that 2 can not be a solution.

15. Now, you do these on your own.