Simplifying Algebraic Fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Simplifying Algebraic Fractions

Mathematics · Algebra · ages 14-15
Name ______________________   Date ____________

  1. For (x squared - 9)/(x - 3), which value of x is not allowed?

    • -3
    • 3
    • 9
    • -9

  2. Simplify (x squared - 4)/(x - 2).

    • x + 2
    • x - 2
    • (x - 2)/(x + 2)
    • x

  3. (x + 5)/(x + 5) simplifies to 1.

    Circle one:   True   False

  4. Simplify (x squared - 1)/(x - 1).

    • x - 1
    • x + 1
    • (x + 1)/(x - 1)
    • x

  5. Simplify (x squared - 6x + 8)/(x - 2).

    • x + 4
    • x - 4
    • x - 2
    • x + 2

  6. For (x squared - 16)/(x squared - 8x + 16), the only excluded value is x = 4.

    Circle one:   True   False

  7. Which of these fractions cannot be simplified?

    • (x squared - 4)/(x - 2)
    • (x squared + 4)/(x + 2)
    • (x squared - 9)/(x + 3)
    • (x squared - 2x)/x

  8. (x squared - 25)/(x + 5) simplifies to x - 5, so x can be -5.

    Circle one:   True   False

  9. (x squared - 2x - 15)/(x squared + 2x - 3) simplifies to (x - 5)/(x - 1). Which excluded value is no longer visible in the simplified form?

    Answer: ______________

  10. A fraction simplifies to x + 5, and its original denominator was x - 1. What was its original numerator?

    • x squared - 4x - 5
    • x squared + 4x + 5
    • x squared + 4x - 5
    • x squared + 9x - 5
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Simplifying Algebraic Fractions W1-mt_scDNSoz3eW-s1

  1. 3 · The excluded value comes from the original denominator x - 3, which is zero when x = 3.
  2. x + 2 · The top is (x - 2)(x + 2). Cancel the shared (x - 2) to get x + 2, with x not equal to 2.
  3. True · The whole bracket (x + 5) is a shared factor, so it cancels and leaves 1, with x not equal to -5.
  4. x + 1 · The top is a difference of two squares: (x - 1)(x + 1). Cancel the shared (x - 1) to get x + 1.
  5. x - 4 · The top is (x - 2)(x - 4). Cancel the shared (x - 2) to get x - 4, with x not equal to 2.
  6. True · The denominator is (x - 4) squared, which is zero only when x = 4.
  7. (x squared + 4)/(x + 2) · The top x squared + 4 cannot be factorised over the integers, so there is no shared factor to cancel.
  8. False · The original denominator x + 5 is zero at x = -5, so the original fraction is undefined there, even though x - 5 is fine.
  9. -3 · The original bottom is (x + 3)(x - 1), so both -3 and 1 are excluded. After cancelling (x + 3), only x = 1 still shows; the excluded value x = -3 has gone invisible.
  10. x squared + 4x - 5 · The numerator must be (x + 5)(x - 1), which expands to x squared + 4x - 5.
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