Practice Simplifying 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

Simplifying a rational expression p(x)q(x) by factoring both the numerator and denominator, then canceling common factors. The domain must exclude values that make any original denominator zero.

Just like simplifying the fraction 68=34 by canceling the common factor of 2, you can simplify x2−4x−2 by factoring the top as (x+2)(x−2) and canceling the common (x−2) factor. But remember: you can only cancel FACTORS (things being multiplied), not TERMS (things being added).

Showing a random 20 of 50 problems.

Example 1

hard
Simplify 2x2+7x+3x2+2x−3, x≠−3,1.

Example 2

medium
Simplify 2x2−8x2+4x+4.

Example 3

easy
Simplify 3x6x2, x≠0.

Example 4

medium
Simplify 3−xx−3, x≠3.

Example 5

medium
Simplify x2−9x2+5x+6.

Example 6

medium
Simplify x2−x−6x2−9 and state restrictions.

Example 7

easy
Simplify 4x22x, x≠0.

Example 8

easy
Simplify 2x+6x+3, x≠−3.

Example 9

challenge
Simplify x4−16x2+4.

Example 10

hard
Simplify x2−3x−10x2−7x+10, x≠2,5.

Example 11

medium
Simplify x2−25x2−10x+25, state restrictions.

Example 12

easy
Simplify x−55−x, x≠5.

Example 13

medium
Simplify x2+7x+12x2+4x, x≠0,−4.

Example 14

easy
Simplify 6x39x, x≠0.

Example 15

hard
Simplify x3−8x2−4, x≠±2.

Example 16

medium
Simplify 3x2−12x2−x−2, state restrictions.

Example 17

challenge
Simplify x2−y2x2−2xy+y2, x≠y.

Example 18

medium
Simplify x3−xx2−1, x≠±1.

Example 19

medium
Simplify x3−xx2−1.

Example 20

challenge
Simplify x3−8x2−4, state restrictions.
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