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Factorise numerator and denominator and cancel to simplify a rational expression

This type of question, asked 3 times: CDS 1 2021, CDS 1 2022, CDS 2 2022. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2021

    11
    The expression (x3−1)(x2−9x+14)(x2+x+1)(x2−8x+7)\frac{(x^3 - 1)(x^2 - 9x + 14)}{(x^2 + x + 1)(x^2 - 8x + 7)} simplifies to

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  2. Question 2

    CDS 1 2022

    9
    If x=9999x = 9999, then what is the value of the following? 4x3−x(2x+1)(6x−3)\frac{4x^3 - x}{(2x + 1)(6x - 3)}

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  3. Question 3

    CDS 2 2022

    12
    What is x6−24x4+144x2(x2+43x+12)(x−23)2\frac{x^6 - 24x^4 + 144x^2}{(x^2 + 4\sqrt{3}x + 12)(x - 2\sqrt{3})^2} equal to ?

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