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.

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 + = 4 ( ) ( ) ( ) ( ) ( ) 5n 4 7 –3 4 + 4 = 4 Distributive Property. 5n + 7 = –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

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

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 + – = 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.

Example 2B Continued 23x – 34 = 12 Combine like terms. + 34 + 34 Add 34 to both sides. 23x = 46 = 23x 23 46 Divide both sides by 23. x = 2

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 + = 4 ( ) ( ) ( ) 3n 4 5 –1 4 + 4 = 4 Distributive Property. 3n + 5 = –1

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

Example 3 Solve. + – = x 3 5x 9 13 1 3 The LCD is 9. ( ) x 3 1 5x 9 13 9 + – = 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.

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