Identifying the type of expression

[mark2142]

TL;DR Summary: ##(1+ \frac1x)^2 - (1-\frac1x)^2##
##(z+2)^2 -5(z+2)##

Upon simplifying the first I get ##\frac4x##. So isn’t the first expression fractional?
Upon simplifying the second I get a Quadratic expression.

 

[BvU]

1. If you want to call it that, yes. One could also say that constant and square terms cancel.
2. I get a product -- matter of taste which is simpler

##\ ##

 

[mark2142]

Thanks man :)

 

[mark2142]

What about ##(x^2+3)^{-\frac13} + \frac23 x^2(x^2+3)^{-\frac43}## ? Fractional expression?
or this ##(x^2+3)^{-\frac13} + 2 x^2(x^2+3)^{-\frac43}## ?