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. If the same whole bracket appears in the top and the bottom, it can be cancelled.

    Circle one:   True   False

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

    Circle one:   True   False

  3. Sam says (x + 5)/(x + 2) simplifies to 5/2 by cancelling the x terms. Is Sam right?

    Circle one:   True   False

  4. What is the first move when simplifying an algebraic fraction like (x squared - 9)/(x + 3)?

    • Take the square root of the top
    • Factorise the top and the bottom
    • Divide the top by the bottom
    • Expand any brackets

  5. For which x values is (x² - 9)/(x² + 7x + 12) undefined?

    • x = -3 or x = -4
    • x = 3 or x = -3
    • x = -4 only
    • x = 3 or x = 4

  6. Sam simplifies (x squared + 5x)/(x + 5) by cancelling the x's and the 5's, and writes x + 5. What went wrong?

    • He cancelled single terms inside a sum; the top is x(x + 5), so the answer is x
    • The top should have been factorised as (x + 5) squared
    • The answer should have been x squared
    • Nothing went wrong

  7. Simplify (x squared + x - 6)/(x - 2).

    • x - 3
    • x + 2
    • (x + 3)(x - 2)
    • x + 3

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

    Circle one:   True   False

  9. Simplify (x cubed - 9x)/(x squared - 9).

    • x
    • x - 3
    • (x - 3)(x + 3)
    • x(x - 3)

  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. True · A whole factor that appears in both parts cancels, leaving the rest of each part.
  2. True · The whole bracket (x + 5) is a shared factor, so it cancels and leaves 1, with x not equal to -5.
  3. False · Sam is wrong. The x terms are parts of a sum, not whole factors, so they cannot be cancelled.
  4. Factorise the top and the bottom · You need to see the factors before you can cancel them, so factorise the top and the bottom first.
  5. x = -3 or x = -4 · The bottom factors into (x + 3)(x + 4), which is zero when x = -3 or x = -4.
  6. He cancelled single terms inside a sum; the top is x(x + 5), so the answer is x · The x in the top is a term, not a factor. The top is x(x + 5), so the whole bracket (x + 5) cancels and the answer is x, with x not equal to -5.
  7. x + 3 · The top is (x + 3)(x - 2). Cancel the shared (x - 2) to get x + 3, with x not equal to 2.
  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. x · The top is x(x - 3)(x + 3) and the bottom is (x - 3)(x + 3), so both brackets cancel and x remains, with x not equal to 3 or -3.
  10. x squared + 4x - 5 · The numerator must be (x + 5)(x - 1), which expands to x squared + 4x - 5.
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