Simplify (x² − 9)/(x − 3).
- The original denominator excludes x = 3.
- Factor x² − 9 = (x − 3)(x + 3); cancel the common factor.
Answer: x + 3, with x ≠ 3
Simplifying Rational Expressions Worksheets
Simplify rational expressions, solve rational equations and retain excluded domain values.
Learn the skill
Simplifying rational expressions and keeping restrictions
A rational expression is a quotient of polynomials. Factor the numerator and denominator, cancel common nonzero factors, and retain every restriction from the original denominator.
A method you can use
- Set the original denominator unequal to zero and record excluded values.
- Factor both polynomials completely.
- Cancel common factors, not individual terms, while keeping the original restrictions.
Worked examples
Simplify (6x²)/(3x).
- The original denominator excludes x = 0.
- Divide coefficients and cancel one factor of x.
Answer: 2x, with x ≠ 0
Can (x + 2)/x be simplified to 2?
- The numerator is a sum, not a product with a common factor x.
- Split the fraction only as x/x + 2/x, where x ≠ 0.
Answer: No; it equals 1 + 2/x
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Simplify (x² − 16)/(x − 4), including restrictions.
Show answer and explanation
x + 4, with x ≠ 4
Factor the numerator as (x − 4)(x + 4).
2. Simplify 8x²/(4x), including restrictions.
Show answer and explanation
2x, with x ≠ 0
Cancel 4 and one x; the original denominator cannot be zero.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Simplify (x² − 4)/(x − 2). State the excluded value from the original expression.
2
Simplify (x² − 36)/(x − 6). State the excluded value from the original expression.
3
Simplify (x² − 49)/(x − 7). State the excluded value from the original expression.
4
Simplify (x² − 25)/(x − 5). State the excluded value from the original expression.
5
Simplify (x² − 64)/(x − 8). State the excluded value from the original expression.
6
Simplify (x² − 1)/(x − 1). State the excluded value from the original expression.
Answer Key
1. x + 2; x ≠ 22. x + 6; x ≠ 63. x + 7; x ≠ 74. x + 5; x ≠ 55. x + 8; x ≠ 86. x + 1; x ≠ 1