Sorry, this is making me crazy. Thank you for pointing out my error.

Question

w-4/w-9 – w+1/w+9 + w-99/w^2 – 81 =

Answer 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

Answer 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)