1. Solving Rational Equations

2. Hint for solving: Check for non-permissible values
A quick way to solve a rational equation is to multiply everything through by the LCD.
Beware of extraneous solutions! Check left side = right side

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. Solving Rational Functions Graphically Using Your Calculator
Method 1: Use a single function and find the x-intercepts.
How? Move everything to one side and make it = 0
Enter your function into your calculator. Use the “Calc” button to find the zeros (x-intercepts)
Method 2: Use a system of 2 functions and find the points of intersection.
How? Enter left side into y1 and right side into y2. Use the “Calc” button to find the intersection point of the two functions.