Rules for manipulating differential/ Leibniz notation? What are the rules on manipulating Leibniz Notation?
dy/dt  = -(y-3)/2
Can I treat it like a fraction and do this?
dy = -(y-3)/2 dt
can I "convert" the dy into a derivative?
(dy/dt)(1/(y-3)) = -1/2
->  d/dt ln|y-3| = -1/2
Where can i find more information on how to manipulate these infinitesimals?

These rules are shortcuts derived from your everyday rules of calculus.  For instance:
$$\frac{dy}{dt} = f(y)$$
Integrate with respect to $t$ to get $\int dy = \int f(y) dt$, or in other words "$dy = f(y) dt$" which means basically $dy$ can be replaced by $f(y)dt$ in an integeral.
