Deriving (∂H/∂P)T using compressibility factor Z

[allover]

Hi all, first post so I hope this is ok to go here. It's not a homework question, just something in my book I don't get...

I am looking through my thermodynamics textbook (Smith,Van Ness, and Abbot, Intro to Chemical Eng thermodynamics) and they give the eq (6.19):

($$\partial$$H/$$\partial$$P)_T = V - T($$\partial$$V/$$\partial$$T)_P

then, "because V = ZRT/P we can write more concisely:

($$\partial$$H/$$\partial$$P)_T = -RT²/P (($$\partial$$Z/$$\partial$$T)_P)

Can anyone explain to me how they did that? I'm sure there is just some simple substitution I am missing

 

[allover]

Nevermind, I went about it by dH/dP = d(U+PV)/dP and it worked out. If an admin can delete this, that would be great.