Explain Adding Rational Expressions with Different Denominators

When you add or subtract fractions or rational expressions that have different denominators, you must first find a common denominator before you can add or subtract them.

Here's an example illustrating this idea with simple fractions:

1/6 +5/8 = 1/6 .4/4 +5/8.3/3
= 4/24 +15/24
= 19/24

Actually, any common denominator can be used, but it is sometimes easier if you use the least common denominator (LCD). We can now apply this method, or idea, to add and subtract rational expressions. Study the following examples very carefully.