Polynomials
Adding and subtracting polynomials worksheets
Print a 10-question adding and subtracting polynomials worksheet. Choose two or three grouped polynomials with four to nine terms and worked answers.
Preview and downloadRational expressions practice
Adding and subtracting rational expressions worksheets
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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Add or subtract. 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 sums and differences. Common-denominator practice includes multivariable monomials and univariate binomials through degree six. Unlike practice combines constant and linear denominators or two distinct linear denominators.
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
Combine two rational expressions and reduce the result without losing values excluded by either original denominator.
Worked example
Simplify x/(x + 1) − 1/x.
(x² − x − 1)/(x(x + 1)), with x + 1 ≠ 0 and x ≠ 0.
Multiply each numerator by the other denominator, subtract in order and retain both original conditions even if later cancellation occurs.
Teaching notes
Make the practice count
- For a common denominator, combine the numerators before reducing.
- For unlike denominators, show both cross-products before collecting terms.
- Keep subtraction parentheses until every sign has been distributed.
- Write restrictions from the original denominators before canceling factors.
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Choose the operations and denominator types, then change the seed for a reproducible set of ten rational expressions.
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