1. Solving Rational Equations
Section 7.5

2. Hint for solving:
A quick way 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!

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

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

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

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

7. Example: Solve.
Check your solutions!

8. Last Example: Solve.
Check your solutions!

9. Example:
A car travels 500 miles in the same time that a train travels 300 miles. The speed of the car is 30 miles per hour faster than the speed of the train. Find the speed of the car and the train.

10. Remember the formula d=rt where:
r = rate of speed
d = distance
t = time
Since both vehicles travel the same amount of time, solve the formula for t.

11. Identify the variables that you are going to use.
Let r = speed of the train
How do you represent the speed of the car?
Let r+30 = speed of the car

12. Car’s time =
Train’s time

13. How would you solve this equation?
Cross-multiply

14. Make sure that you answer the question.
The car travels at a speed of 75mph
The train travels at a speed of 45 mph