Inequality With Exponent 3 and a Fraction

Oct 2013
713
91
New York, USA
Solve x^2 + x/(x^2) < x^3

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.
 

skeeter

Math Team
Jul 2011
3,355
1,848
Texas
Pretty sure one would need technology to calculate the solution set of this inequality.