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Simplify a fraction using a^2 - b^2 = (a - b)(a + b) and cancel

This type of question, asked 6 times: 17 Jul 2023 S2, 20 Jul 2023 S1, 25 Jul 2023 S2, 25 Jul 2023 S4, 9 Sep 2024 S1, 26 Sep 2024 S3. All 6 questions below, oldest first.

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  1. Question 1

    17 Jul 2023 S2

    71
    Simplify, x4−2x2+1x2−2x+1\frac{x^4 - 2x^2 + 1}{x^2 - 2x + 1}.

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  2. Question 2

    20 Jul 2023 S1

    65
    Simplify the expression l2−m2(l+m)2\frac{l^2 - m^2}{(l + m)^2}, provided (l+m)≠0(l + m) \ne 0.

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  3. Question 3

    25 Jul 2023 S2

    70
    Simplify 256x4−16y4(80x2−20y2)(16x2+4y2)\frac{256x^4 - 16y^4}{(80x^2 - 20y^2)(16x^2 + 4y^2)}.

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  4. Question 4

    25 Jul 2023 S4

    61
    Simplify the expression s2+t2+2st−u2s2−t2−2tu−u2\frac{s^2 + t^2 + 2st - u^2}{s^2 - t^2 - 2tu - u^2}, provided (s+t+u)≠0(s + t + u) \ne 0.

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  5. Question 5

    9 Sep 2024 S1

    65
    Simplify (x2−9)x+3\frac{(x^2 - 9)}{x + 3}

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  6. Question 6

    26 Sep 2024 S3

    72
    Simplify 4x2−49y22x+7y+7y−2x\frac{4x^2 - 49y^2}{2x + 7y} + 7y - 2x

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