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A tough inequality question!

find x which allows this inequality to hold:
1+2x-x^2>2/x

So I thought since, we don't know if x is negative or positive create 2 cases. Case 1) where x is negative and therefore x+2x^2-x^3<2, and solve
or case 2) where x is positive and therefore x+2x^2-x^3>2

Then working out the solutions to each and finding which set of x values satisfy the equation?

If you can't help me with the actual equation, please let me know if my idea seems sensible or if it is flawed. Thanks!