Rational expressions
Solving rational equations worksheets
Practice ten exact rational equations with monomial or binomial expressions, original-domain restrictions and checked rational solutions.
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Dividing rational expressions worksheets
Practice ten exact quotients with expanded monomials, linear binomials and factorable quadratics, fully reduced answers and all original domain restrictions.
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Divide and simplify. Keep both original denominators and the divisor numerator nonzero.
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Keep all three original division conditions
Each worksheet contains ten quotients shown in expanded form. Choose any combination of monomials, linear binomials and factorable quadratics; the seed keeps the selected family schedule reproducible.
The answer key reduces each reciprocal product exactly and prints the nonconstant restrictions from both original denominators and the divisor numerator. A canceled factor still excludes the values that made the original division undefined.
Learning objective
What this activity builds
Divide two rational expressions, reduce the reciprocal product completely and preserve both original denominator restrictions plus the condition that the divisor numerator is nonzero.
Worked example
Divide (x² − 9)/(x + 1) ÷ (x − 3)/(x + 2).
(x + 3)(x + 2)/(x + 1), with x + 1 ≠ 0, x + 2 ≠ 0 and x − 3 ≠ 0.
Multiply by the reciprocal, factor x² − 9, cancel x − 3 and retain every condition from the two original denominators and the divisor numerator.
Teaching notes
Make the practice count
- Record both original denominator restrictions before simplifying.
- Require the divisor numerator to be nonzero because a zero rational expression cannot be a divisor.
- Multiply by the reciprocal, then factor and cancel complete factors.
- Keep every original restriction even when its factor cancels.
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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 divisions with all original domain conditions.
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Practice ten exact single-quotient reductions with monomial, binomial or trinomial inputs, complete cancellation and retained original denominator restrictions.
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