1. Solving Rational Equations

2. In the previous lessons we worked extensively with solving rational equations with cross-multiplying.
Today we will work with equations that are slightly more complex.

3. 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!

4. Solving Rational Equations
Find the LCD
Multiply every numerator by the LCD
Simplify (denominators will cancel out)
Solve for the variable
Don’t forget to CHECK your solution.

5. Multiply each fraction by the LCD
1. SOLVE
What is the LCD? 9x
Multiply each fraction by the LCD
5x + 2 = 27
5x = 25
x = 5

6. Multiply each fraction by the LCD
2. SOLVE 3x
What is the LCD?
Multiply each fraction by the LCD
12 + 2x = 18
2x = 6
x = 3

7. 3. YOU solve this one… 2x
What is the LCD?

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