Physical chemistry question?

Question

Can't figure this one out:
If the equation of state of a certain gas is
P=(nRT/V) + n(a+bT)/V^2 where a and b are constants, find
(dV/dT) holding P constant.

Answer 1

take the derivative with respect to T

dP/dT = 0 = nR d/dT(T/V) + n d/dT((a+bT)/V^2)

apply quotient rule and chain rules:

0 = nR(V - TdV/dT)/V^2 + n(V^2b - (a+bT)2VdV/dT))/V^4

gather terms:

nRV^3 + nbV^2 = TV^2dV/dT + 2V(a+bT)dV/dT

dV/dT = (nRV^2 + nbV)/(TV + 2(a+bT))

Answer 2

dV/dT = 1