# Adding Rational Expressions with the Same Denominator

Adding rational expressions with the same denominator is like adding fractions with the same denominator.

Procedure â€” To Add Rational Expressions with the Same Denominator

Step 1 Add the numerators. Write this sum as the numerator over the common denominator.

Step 2 Reduce to lowest terms.

Note:

Hereâ€™s an example of adding fractions:

The denominators are the same. Add the numerators and write the sum over the common denominator, 4.

To reduce, cancel the common factor, 2, in the numerator and denominator.

Thus,

Example 1

Find:

Solution

 The denominators are the same. Step 1 Add the numerators. Write this sum as the numerator over the common denominator. Combine the like terms in the numerator. Step 2 Reduce to lowest terms. First, factor the numerator and denominator. Next, cancel the common factor, 5.

Thus,

Example 2

Find:

Solution

 The denominators are the same. Step 1 Add the numerators. Write this sum as the numerator over the common denominator. Combine the like terms in the numerator. Step 2 Reduce to lowest terms. First, factor the numerator and denominator. Next, cancel the common factor, x + 1.

Thus,