To solve this problem, you will have to factor.
You can factor x^4-81 into (x^2+9)(x^2-9) and further with (x^2+9)(x+3)(x-3) because of perfect square trinomial rule.
Then the problem will look like this.
(x^2+9)(x+3)(x-3)/x+3
Now you can simplify by canceling out x+3. Then your simplified form is:
(x^2+9)(x-3)
:)