Google - divide and simplify x^2-3x/x^3-27 ÷ 2x^2+6x+18?

You really should spend some time to learn correct presentation. First, add spaces so the terms don't all run together.

x^2 - 3x/x^3 - 27 ÷ 2x^2 + 6x + 18

Now you can see that "simplify" does not apply. It also looks like you have omitted some parentheses, because what you have here is rather trivial.

Guessing: (x^2 - 3x/x^3 - 27) ÷ (2x^2 + 6x + 18)

Or it could be: (x^2 - 3x/(x^3 - 27)) ÷ (2x^2 + 6x + 18)

Other combinations are possible. But people are not supposed to have to guess at what you meant.