Adding and Subtracting Fractions
6-5Adding and Subtracting Fractions
Overview
Rewrite each fraction with the LCD, then add or subtract the numerators.
Key ideas
- Same denominator → add/subtract numerators.
- Different denominators → find LCD first.
- Simplify the result.
Worked examples
Example 1
Problem. 1/4 + 1/6
Solution. 3/12 + 2/12 = 5/12
Example 2
Problem. 1/x + 1/(x^2)
Solution. x/x^2 + 1/x^2 = (x + 1)/x^2
Practice
Try each one. Click Show answer when ready.
- 1.
1/3 + 1/5
- 2.
1/x − 1/(x+1)
- 3.
(2/x) + (3/x^2)
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify: 3/(x+2) + 5/(x−2).
- 2.
Simplify: (2x)/(x²−9) − 3/(x+3).