1. If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.

2. Example 1
Solve.
+ = – 5n 4 7 4 3 4
Multiply both sides by 4 to clear fractions, and then solve. 7 4 –3 5n
= 4
( ) ( )
( ) ( ) ( ) 5n 4 7 –3
= 4
Distributive Property.
5n + 7 = –3

3. Example 1
5n + 7 = –3
– 7 –7 Subtract 7 from both sides.
5n = –10 5n 5
–10 =
Divide both sides by 5
n = –2

4. The least common denominator (LCD) is the smallest number that each of the denominators will divide into.
Remember!

5. Example 2: Solving Equations That Contain Fractions
Solve.
+ – = x 2 7x 9 17 2 3
The LCD is 18.
( ) ( ) x 2 3 7x 9 17
– = 18
Multiply both sides by 18.
18( ) + 18( ) – 18( ) = 18( ) 7x 9 x 2 17 3
Distributive Property.
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.

6. Example 2B Continued
23x – 34 = Combine like terms.
Add 34 to both sides.
23x = 46 =
23x 23 46
Divide both sides by 23.
x = 2

7. Example 3
Solve.
+ = – 3n 4 5 4 1 4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( ) 5 4 –1 3n
= 4
( ) ( ) ( ) 3n 4 5 –1
= 4
Distributive Property.
3n + 5 = –1

8. Example 2 Solution
3n + 5 = –1
– 5 – Subtract 5 from both sides.
3n = –6 3n 3 –6 =
Divide both sides by 3.
n = –2

9. Example 3
Solve.
+ – = x 3 5x 9 13 1 3
The LCD is 9.
( ) x 3 1 5x 9 13
– = 9( )
Multiply both sides by 9.
9( ) + 9( )– 9( ) = 9( ) 5x 9 x 3 13 1
Distributive Property.
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.

10. Example 3 Solution
8x – 13 = Combine like terms.
Add 13 to both sides.
8x = 16 = 8x 8 16
Divide both sides by 8.
x = 2