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Limit of a difference of two fractions: combine, factorise, cancel

This type of question, asked 2 times: 11 May 2024 S1, 11 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    11 May 2024 S1

    103
    lim⁡x→2(1x−2−2xx3−3x2+2x)\lim_{x \to 2} \left(\frac{1}{x-2} - \frac{2x}{x^3-3x^2+2x}\right) is equal to

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  2. Question 2

    11 Apr 2026 S2

    61
    lim⁡x→1[x−2x2−x−1x3−3x2+2x]=\lim_{x \to 1}\left[\dfrac{x - 2}{x^2 - x} - \dfrac{1}{x^3 - 3x^2 + 2x}\right] =

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