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Factorise a trinomial or cube in a fraction and cancel

This type of question, asked 4 times: 25 Jul 2023 S3, 9 Sep 2024 S1, 13 Sep 2024 S2, 18 Sep 2024 S3. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jul 2023 S3

    52
    Simplify the following expression. x2−2x−63x2+14x+49\frac{x^2 - 2x - 63}{x^2 + 14x + 49}

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  2. Question 2

    9 Sep 2024 S1

    71
    Simplify x3+15x2+75x+125x2−25(x−5)\frac{x^3 + 15x^2 + 75x + 125}{x^2 - 25}(x - 5).

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  3. Question 3

    13 Sep 2024 S2

    70
    Simplify 25a2−10ab−48b25a+6b×(5a+8b)\frac{25a^2 - 10ab - 48b^2}{5a + 6b} \times (5a + 8b)

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  4. Question 4

    18 Sep 2024 S3

    61
    Simplify the given expression. (4x2+9y2−12xy)(3y−2x)\frac{(4x^2 + 9y^2 - 12xy)}{(3y - 2x)}.

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