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Rational expressions practice

Simplifying rational expressions worksheets

Practice ten exact single-quotient reductions with monomial, binomial or trinomial inputs, complete cancellation and retained original denominator restrictions.

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Simplify each rational expression completely and keep the original denominator restriction.

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Keep the original domain while simplifying

Each worksheet contains ten single rational expressions. Choose monomial, up-to-binomial or up-to-trinomial practice to control the largest original polynomial shape.

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

Reduce a rational expression completely while preserving every value excluded by its original denominator.

Worked example

Simplify (x² − 9)/(x + 3).

x − 3, with x + 3 ≠ 0.

Factor the numerator as (x − 3)(x + 3), cancel the common factor and retain the original denominator restriction.

Teaching notes

Make the practice count

  • Factor the numerator and denominator before canceling.
  • Cancel complete factors rather than individual terms.
  • Normalize the final denominator to a positive leading coefficient.
  • Record the original denominator restriction before reducing.

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Choose the largest original polynomial type, then change the seed for a reproducible set of ten quotients.

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Math SheetNameScore/ 10TeacherDateSimplifying Rational ExpressionsSimplify each rational expression completely and keep the original denominator restriction.1.-3x2-6x-3x2+4x+32.-6q-1812q2+44q+243.-2y-2y+14.-9-3r+65.8q212q66.4s42s37.18z2-60z+18-9z+38.12p-30-16p2-8p+1209.3n2+9n-543n2-4n-1510.9p2-21p+12-p+1math-sheet.comPage 1 / 1

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