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Worksheets›Algebra 2›Rational expressions & functions›Simplifying rational expressions

Simplifying 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.6Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: A common binomial factor

  1. 1.3x2 − 6x − 45x2 − 11x + 30
  2. 2.x2 − x − 2x2 + 4x + 3
  3. 3.2x2 − 18x + 36x2 − 4x + 3
  4. 4.5x2 + 50x + 120x2 − 2x − 24
  5. 5.3x2 − 33x + 84x2 − 7x
  6. 6.2x2 − 4x − 48x2 − 8x + 12
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

Factor the numerator and the denominator completely, then cancel factors that appear in both. Only whole factors cancel, never single terms. The excluded values make the original denominator zero, including any factor that was cancelled.

Easy3x2 − 27x2 − 4x − 21A common binomial factorMediumx2 − 10x + 21x2 − x − 6Trinomials over trinomialsHard−x2 + x + 20x2 + x − 12Opposite factors such as (x − 3) and (3 − x)

How to solve it: a worked example

Simplify. State the values of x that are excluded.

  1. Startx2 − x − 2x2 + 4x + 3
  2. Factor the top and the bottom(x + 1)(x − 2)(x + 1)(x + 3)
  3. Cancel the common factorx − 2x + 3
  4. Exclude the zeros of the original denominatorx ≠ −3, −1
  5. Answerx − 2x + 3; x ≠ −3, −1

Common mistakes to watch for

  • Cancelling terms instead of factors, such as the x² in (x² + 3)/(x² + 5).
  • Forgetting the excluded value from a factor that cancelled.
  • Missing that (3 − x) = −(x − 3).

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

Related worksheets

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

FAQ

Why can't you cancel the x in (x + 3)/x?

Only common factors cancel, and x + 3 is a sum, not a product. Factor the top and bottom first, then cancel whole factors.

Why state excluded values?

The original expression is undefined wherever its denominator is 0, even if that factor cancels. (x² − 4)/(x − 2) simplifies to x + 2, but x ≠ 2.

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 simplifying 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.