Practice Adding and Subtracting Rational Expressions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Adding or subtracting rational expressions by finding a least common denominator (LCD), rewriting each fraction with the LCD, then combining the numerators over the common denominator.

Just like 13+14 requires a common denominator of 12, adding 2x+1+3x−2 requires the LCD (x+1)(x−2). Rewrite each fraction so both have the same denominator, then add the numerators. The process mirrors numeric fractions but with polynomial denominators.

Showing a random 20 of 50 problems.

Example 1

medium
Add 5x+3x−2, x≠0,2.

Example 2

hard
Combine xx2−9+1x−3−1x+3 for x≠±3.

Example 3

medium
Add 2x+1+3x−2, x≠−1,2.

Example 4

medium
Subtract x+1x−x−1x+1, x≠0,−1.

Example 5

challenge
Subtract xx2−x−6−2x−3, x≠3,−2.

Example 6

challenge
Add 3x−2+2x+2+1x2−4, x≠±2.

Example 7

medium
For what value(s) of x is 1x−3+1x+3 undefined?

Example 8

easy
Add 3x+2x2, x≠0.

Example 9

hard
Find the value of 1x−2+1x+2 at x=3.

Example 10

medium
Subtract 1x+2−1x−2 for x≠±2.

Example 11

medium
Add 2x−1+3x+2 for x≠1,−2.

Example 12

easy
Simplify 2xx+1−x−1x+1 for x≠−1.

Example 13

hard
Combine 1x+1x+1+1x+2 for x≠0,−1,−2.

Example 14

medium
Add 1x+2x2+3x3, x≠0.

Example 15

medium
Combine 2x2−3x3 for x≠0.

Example 16

medium
Add 2x+1+3x−2.

Example 17

medium
Worked example: combine 3x2−4+1x−2 for x≠±2.

Example 18

medium
Subtract xx−3−3x−3 and simplify, x≠3.

Example 19

medium
Subtract 5x−3−2x+1.

Example 20

medium
Add xx−2+2x+2 for x≠±2.
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