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Worksheets›Algebra 2›Rational expressions & functions›Multiplying and dividing rational expressions

Multiplying and Dividing Rational Expressions Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 2CCSS HSA.APR.D.7Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Multiplying

  1. 1.x2 − 4xx2 + 6x + 5 × x + 5x − 4
  2. 2.x2 − xx2 − 2x − 3 × x − 3x
  3. 3.x2 + 6xx2 − 6x + 8 × x − 2x + 6
  4. 4.x2 + x − 12x2 + 2x × x + 2x + 4
  5. 5.x2 − 4x − 12x2 + x − 30 × x + 6x + 2
  6. 6.x2 + 3x − 10x2 − 36 × x − 6x − 2
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Factor every numerator and denominator first. To multiply, multiply across and cancel factors that appear on the top and the bottom. To divide, multiply by the reciprocal of the second expression. The excluded values make any denominator zero, including the numerator of a divisor, since it ends up on the bottom.

Easyx2 − 5x + 6x2 − 16 × x − 4x − 2MultiplyingMediumx2 + 3x − 10x2 + 6x + 8 ÷ x − 2x + 4DividingHardx2 − 16x2 − 25 ÷ x + 4x + 5Mixed, with larger numbers

How to solve it: a worked example

Multiply or divide. Simplify, and state the excluded values.

  1. Startx2 − 11x + 30x2 − x × x − 1x − 6
  2. Factor(x − 5)(x − 6)(x − 1)x × x − 1x − 6
  3. Cancel the common factorsx − 5x
  4. Exclude values that make a denominator zerox ≠ 0, 1, 6
  5. Answerx − 5x; x ≠ 0, 1, 6

Common mistakes to watch for

  • Cancelling before flipping the divisor.
  • Flipping the first expression instead of the second.
  • Forgetting that the divisor's numerator can't be zero either.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Simplifying rational expressionsAdding and subtracting rational expressionsSolving rational equationsAsymptotes and holes of rational functionsOperations with complex numbers

FAQ

Should you multiply out before cancelling?

No. Factor everything first and cancel common factors across the tops and bottoms; multiplying out first makes the factors hard to see.

How do you divide rational expressions?

Multiply by the reciprocal of the second expression, then factor and cancel, just as with numeric fractions.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix multiplying and dividing rational expressions with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.