I haven’t had my differential equations class yet and I’m not sure if it’s mathematically okay to do this (originally I’ve obtained this equation from some thermodynamics law but it’s not SUPER relevant here):
$\frac{\delta E}{T} = \frac{P\delta V}{T}$
$\delta E = P \delta V$
Can I just cancel out the $\frac{1}{T}$ term, despite different differentials?
As long as $dT$ is not one of the differentials, it should be okay to cancel out $\frac{1}{T}.$