Multiplying every term by x^2 makes x^4 + x < x^5

Moving everything to the left makes -x^5 + x^4 + x < 0

Dividing everything by x makes -x^4 + x^3 + 1 < 0. Diving by x is okay because if x = 0, the original inequality is undefined, so x < or > 0.

Moving the 1 to the right makes -x^4 + x^3 < -1

Factoring x^3 makes x^3(-x + 1) < -1

I don't know if all of that is useful, but even if it is, I don't know how to do more.