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Handle algebraic fractions three ways. Simplify one by factorising the top and the bottom and cancelling whole brackets, combine two by writing them over a common denominator, or solve an equation containing them by multiplying through. Each step is shown with the fractions stacked exactly as they would be written on paper.

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Method, Step by Step

    Worked Example

    Simplify (x² − 9) ÷ (x² + x − 6).

    1. Factorise the top, a difference of two squares: (x − 3)(x + 3)
    2. Factorise the bottom: (x + 3)(x − 2)
    3. Cancel the shared bracket (x + 3)

    Answer: (x − 3) ÷ (x − 2)

    Try These Yourself

    Simplify (2x + 6) ÷ (x² + 5x + 6).Show answerHide answer

    Answer: 2 ÷ (x + 2)

    2(x + 3) on the top, (x + 3)(x + 2) on the bottom.

    Write 1 ÷ (x + 1) + 1 ÷ (x + 2) as a single fraction.Show answerHide answer

    Answer: (2x + 3) ÷ ((x + 1)(x + 2))

    Top: (x + 2) + (x + 1) = 2x + 3.

    Solve 2 ÷ (x + 1) + 3 ÷ (x + 2) = 2.Show answerHide answer

    Answer: x = −1.5 or x = 1

    2(x + 2) + 3(x + 1) = 2(x + 1)(x + 2) gives 2x² + x − 3 = 0.