Lesson 3

You saw in Try This 5 that when adding rational expressions with different denominators, you need to first find a common denominator. Adding Fractions illustrates this process.

Consider the following example:

The first step is always to state the non-permissible value. Looking at the denominators, you can see that a ≠ 0.

Next, find the lowest common denominator. Find the prime factorization of each denominator.

15a = 3 × 5 × a

5a2 = 5 × a × a

Therefore, the LCD is 3 × 5 × a × a = 15a2.

Multiply each expression by a fraction that is equal to 1, so each expression has the denominator 15a2.

Now each denominator is the same. Simplify.

Subtract the numerators.

Make sure to include the restrictions from the original expressions.

Self-Check 2