Sorry, this is making me crazy. Thank you for pointing out my error.
w-4/w-9 – w+1/w+9 + w-99/w^2 – 81 =

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  1. (w-4)/(w-9) – (w+1)/(w+9)
    + (w-99)/(w^2 – 81)
    = [(w-4)(w+9)-(w+1)(w-9)+(w-99)]/[(w-9)(w+9)]
    = [w^2+5w -36 -w^2 +8w +9 +w -99]/[(w-9)(w+9)]

    = [14w -72]/[(w-9)(w+9)]
    = 2(7w -36)/[(w-9)(w+9)]
    I don't see any further simplifications

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  2. = [w^2+5w -36 -w^2 +8w +9 +w -99]/[(w-9)(w+9)]

    = [14w -126]/[(w-9)(w+9)]
    = 14(w-9)/[(w-9)(w+9)]
    = 14/(w+9)

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