How do i do this complex fracton?

Question

3 w^-1

____________

9w-w^-1

Answer 1

(3w^-1) / (9w - w^-1) = ?

Multiply both top and bottom by w to get rid of that w^-1 (i.e., (w)(w^-1) = 1).

((w)(3w^-1) / (w)(9w - w^-1) = (3) / (9w^2 - 1) = (3) / (3w + 1)(3w - 1)