You Would Not Believe This (Neither Did I)

You may not believe it, but that was the inequality plot for

(3p^2 - 4p + 2)/[p(p - 1)] < (3x^2 + 2x + 1)/[x(x + 1)]



Additionally:

is the inequality plot for:

(3p^2 - 4p + 2)/[p(p - 1)] < (3x^2 + 2x + 1)/[x(x + 1)], x >= 5


Lastly (and this was the best one -- I literally fell off my seat when I saw this):

This is (and you would not believe this -- neither did I) the inequality plot for...




























ARE YOU READY?
















It was the INEQUALITY PLOT for:

(3p^2 - 4p + 2)/[p(p - 1)] < (3x^2 + 2x + 1)/[x(x + 1)], x >= 5, p = x











=)   =)   =)   =)   =)   =)














Please click on ALL THOSE hyperlinks to the respective WolframAlpha computations that I did in the many hours that have passed, to see the inequality plots (and the corresponding solutions) as given by WolframAlpha.

My profuse thanks to Wolfram Research for coming up with WolframAlpha -- the only computational knowledge engine that I know which has far exceeded my expectations!  =)