Perform the indicated operation and simplify w-8/w-9 -w+1/w-9 +w-27/w^2-81?

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Vin Ginge answered
(w-8/w-9)  - (w+1/w-9)  + (w-27/w2-81)
As the first two terms have the same denominator they can be combined :
(w-8/w-9)  - (w+1/w-9) = -9 / w - 9
The denominator for the third term can be factored :- (w-27/w2-81) = w - 27 / (w + 9)(w - 9)
Combining the new expressions gives :-
-9 /(w - 9) + (w - 27/(w + 9)(w - 9)
Now multiply the first term by (w + 9) to provide a common denominator
-9(w + 9) / (w - 9)(w + 9) + (w - 27/ (w + 9)(w - 9) = -9w - 81 + w - 27 / (w + 9)(w - 9) = -8w - 108 / (w + 9)(w - 9)
This can be simplified to :  -4(2w + 27) / (w2 - 81)

Note : The answer is based on the original terms being as expressed in the top line of the answer. If this is incorrect then the eventual answer may be different.

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