Question

(4m-9n-9n^2÷16m^2)+1÷4m-3n

Answer 1

8m - 12n - 9n^2 + 16m^2 + 1,
16m^2 + 8m - 9n^2 - 12n + 1,
8m(2m + 1) - 3n(3n + 4) + 1,

Answer 2

as written, using PEMDAS, this parses out as
(4m-9n-9n^2÷16m^2)+1÷4m-3n
= 4m - 9n - (9n^2/16m^2) + 1/(4m) - 3n

Maybe you meant
((4m-3n-9n^2)÷16m^2 + 1)÷(4m-3n)
= (4m-3n-9n^2+16m^2)÷(16m^2(4m-3n))
= (4m-3n+(4m-3n)(4m+3n)) ÷ (16m^2(4m-3n))
= (4m-3n)(4m+3n+1) ÷ (16m^2(4m-3n))
= (4m+3n+1) ÷ 16m^2
That's not quite what you had, but maybe if you used some of your own parentheses, things would be clearer