Since you know PV= RT where R is the gas constant, with P, V and T variables, you know that


[tex]\frac{{PV}}{T} = R = {\rm{a}}\;{\rm{constant}}[/tex]


We can rearrange this


[tex]\left( {\frac{{PV}}{T} - R} \right) = {\rm{0}}[/tex]

Isn't this now in the format you seek?

However noting your other threads about Van der Waal's equation I wonder if your book was leading up to some more complicated function of P, V and T such as VDW.