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Algebraic fractions Cambridge IGCSE Mathematics (9–1) revision

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In plain words

A fraction with letters in it follows exactly the same rules as one with numbers. To simplify, cancel things that are on both the top and the bottom. The catch is that you can only cancel factors, so you usually have to factorise first.

Three things to know

  1. Simplify by factorising the top and the bottom, then cancelling any bracket that is in both.
  2. To add or subtract, give the fractions a common denominator, just as with numbers.
  3. To multiply, multiply tops and bottoms. To divide, flip the second fraction and multiply.

Worked example

Simplify (x² − 4) ÷ (x² + 5x + 6).

  1. Factorise the top: x² − 4 = (x − 2)(x + 2).
  2. Factorise the bottom: x² + 5x + 6 = (x + 2)(x + 3).
  3. Cancel (x + 2): the answer is (x − 2)/(x + 3).

Tips and tricks

  • You can't cancel across a plus or minus sign. In (x + 3)/3 the 3s don't cancel.
  • For a common denominator, multiply the two denominators together: it always works.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Algebraic fractions: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is 6x/3 simplified?
    • 3x
    • 2x (the answer)
    • 2
    • 18x

    6 ÷ 3 = 2.

  2. What is (x² + x)/x simplified?
    • x²
    • x
    • x + 1 (the answer)
    • 2x

    Factorise the top: x(x + 1), then cancel x.

  3. What is x/4 + x/4?
    • x/8
    • x/2 (the answer)
    • 2x/8
    • x²/4

    2x/4, which cancels to x/2.

  4. What is 1/x + 1/y as a single fraction?
    • 2/(x + y)
    • 1/(xy)
    • (x + y)/(xy) (the answer)
    • 2/(xy)

    y/(xy) + x/(xy).

  5. What is (4x + 8)/4 simplified?
    • x + 8
    • x + 2 (the answer)
    • 4x + 2
    • x + 4

    4(x + 2)/4.

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