Simplifying Rational Expressions Worksheet + Practice Generator
Practice simplifying rational expressions by the factoring process required: GCF, difference of squares, trinomial factoring, grouping, and sign reversal. Includes 18 problems, a one page quick guide, an interactive question generator, and an answer key.
Free for classroom, tutoring, homework, and Algebra review.
Simplifying Rational Expressions Quick Guide
The order matters: find restrictions from the original denominator, factor completely, cancel common factors, rewrite, and keep every original restriction.
Download the one-page printable guide →
Worked example: factor first, then simplify
x² - 5x + 6x² - 9
x² - 9 = 0, so x ≠ 3, -3.
(x - 2)(x - 3)(x - 3)(x + 3)
The factor cancels algebraically, but x = 3 remains excluded from the original expression.
x - 2x + 3 with x ≠ 3, -3.
Rational Expression Practice Generator
Make new questions to practice with so you never run out of practice problems for a future test or quiz.
Ready To Use Practice Problems
Each part will help you get more experience with a different skill. My students usually like studying like this where they reinforce one skill and move onto the next one when they are ready. You can also do questions out of order for general practice.
GCF & Common Factors
Pull out numerical or variable GCFs first.
Difference of Squares
Recognize conjugate factors and repeated binomials.
Trinomial Factoring
Factor monic and non-monic quadratics completely.
Grouping & Sign Reversal
Use grouping or pull out -1 when factors look reversed.
GCF & Common Factors
Factor out numerical or variable GCFs before cancelling.
Difference of Squares & Repeated Factors
Recognize a² - b² and repeated binomial factors before simplifying.
Trinomial & Non-Monic Factoring
Factor monic and non-monic quadratics, then cancel complete factors.
Grouping & Sign Reversal
Use grouping or a sign reversal when the common factor is not immediately obvious.
Simplifying Rational Expressions Worksheet Answer Key
The printable key mirrors the worksheet format and shows the factoring step directly beneath each problem. Every restriction still comes from the original denominator.
| # | Part | Simplified form | Excluded values | Factored form |
|---|---|---|---|---|
| 1 | Part A | 2x/3 | x ≠ 0 | (3x)(2x) / [(3x)(3)] |
| 2 | Part A | x + 5 | x ≠ 0 | x(x + 5) / x |
| 3 | Part A | x + 4 | x ≠ 0 | 2x(x + 4) / 2x |
| 4 | Part A | (x - 4)/2 | x ≠ 0 | 3x(x - 4) / 6x |
| 5 | Part B | x - 3 | x ≠ -3 | (x - 3)(x + 3) / (x + 3) |
| 6 | Part B | (x + 4)/(x - 4) | x ≠ 4 | (x - 4)(x + 4) / (x - 4)² |
| 7 | Part B | 3(x + 2)/(x + 3) | x ≠ 2, -3 | 3(x - 2)(x + 2) / [(x - 2)(x + 3)] |
| 8 | Part B | x(x + 3)/(x - 3) | x ≠ 3 | x(x - 3)(x + 3) / (x - 3)² |
| 9 | Part B | 2(x - 3)/(x + 3) | x ≠ -3 | 2(x - 3)(x + 3) / (x + 3)² |
| 10 | Part C | (x + 2)/(x + 3) | x ≠ 2, -3 | (x - 2)(x + 2) / [(x - 2)(x + 3)] |
| 11 | Part C | (x - 2)/(x + 3) | x ≠ 3, -3 | (x - 2)(x - 3) / [(x - 3)(x + 3)] |
| 12 | Part C | (x + 3)/(x + 1) | x ≠ -4, -1 | (x + 3)(x + 4) / [(x + 1)(x + 4)] |
| 13 | Part C | (2x + 3)/(2x - 3) | x ≠ 1, 3/2 | (2x + 3)(x - 1) / [(2x - 3)(x - 1)] |
| 14 | Part C | (2x - 5)/(x + 1) | x ≠ -5/2, -1 | (2x - 5)(2x + 5) / [(2x + 5)(x + 1)] |
| 15 | Part D | x(x - 2)/(x - 3) | x ≠ -2, 3 | x(x - 2)(x + 2) / [(x - 3)(x + 2)] |
| 16 | Part D | -(x + 2) | x ≠ 2 | (x - 2)(x + 2) / [-(x - 2)] |
| 17 | Part D | x - 3 | x ≠ -2, -3 | (x + 2)(x - 3)(x + 3) / [(x + 2)(x + 3)] |
| 18 | Part D | x - 4 | x ≠ -1, 1 | (x - 4)(x - 1)(x + 1) / [(x - 1)(x + 1)] |
Common Simplifying Rational Expressions Mistakes
Cancelling terms instead of factors
In (x + 3)/x, the x does not cancel. x + 3 is a sum, not a product containing x as a factor.
Dropping excluded values
A denominator factor can cancel and still leave its original x-value excluded.
Missing a sign reversal
2 - x = -(x - 2). Reversed binomials differ by a factor of -1.
Related Algebra Worksheets and References
Additional free education references
Created and reviewed by Berke Sahbazoglu
Owner and lead tutor, Burke Tutoring in Fremont. 10+ years of tutoring experience and 6,000+ tutoring hours across K-12 math and science, including extensive Algebra I & II instruction. These problems were adapted from rational-expression practice I use with students and independently checked before publication. This resource was reviewed for factoring, cancellation, sign handling, and excluded values from every original denominator.