Rational expressions
Dividing rational expressions worksheets
Practice ten exact quotients with expanded monomials, linear binomials and factorable quadratics, fully reduced answers and all original domain restrictions.
Preview and downloadRational expressions practice
Multiplying rational expressions worksheets
Practice ten exact products using monomials, binomial factors and factorable polynomials, with reduced answers and retained original denominator restrictions.
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Multiply. Write each answer in fully reduced form and keep the original denominator restrictions.
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Keep the original domain while simplifying
Each worksheet contains ten products. Choose any combination of monomials, binomial factors and factorable polynomials; the seed keeps the selected family schedule reproducible.
The answer key reduces every result exactly and prints each nonconstant original denominator restriction. A canceled factor still excludes the values that made the original expression undefined.
Learning objective
What this activity builds
Multiply two rational expressions, reduce the product completely and preserve every value excluded by either original denominator.
Worked example
Multiply (x² − 9)/(x + 3) × (x + 1)/(x − 2).
(x − 3)(x + 1)/(x − 2), with x + 3 ≠ 0 and x − 2 ≠ 0.
Factor x² − 9, cancel the common x + 3 factor and retain both original denominator restrictions.
Teaching notes
Make the practice count
- Factor each numerator and denominator before canceling.
- Cancel common factors across the complete product, not terms within a sum.
- Multiply the remaining numerator factors and denominator factors.
- Keep restrictions from both original denominators even after cancellation.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more expression families, then change the seed for a reproducible set of ten products.
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Practice ten exact sums and differences with common or unlike polynomial denominators, including multivariable monomials, higher-degree binomials and retained domain restrictions.
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