Subtracting Rational Expressions with the Same Denominator

Subtracting rational expressions with the same denominator is like subtracting fractions with the same denominator.

Procedure — To Subtract Rational Expressions with the Same Denominator

Step 1 Subtract the numerators. Write the difference as the numerator over the common denominator.

Step 2 Reduce to lowest terms.

 

Note:

Here’s an example of subtracting fractions:

Subtract and write the answer in lowest terms:

The denominators are the same.

Subtract the numerators and write the difference over the common denominator, 6.

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

Thus,

 

Example 1

Find:

Solution

Thus,

 

Example 2

Find:

Solution

Thus,