Is PV=nRT another way to the same as dividing n into both denominators in the combined gas law?

Like, in any scenario (if I needed to find P, V, n or T), will I get the same answer as if I used PV=nRT if I do this?

P1V1/T1n1=p2V2/T2n2

Not exactly, n does not change in the classic gas problems, so n1=n2 and

P1V1/T1 = P2V2/T2

If there is a reaction and the moles change, the problems are worked a slightly different way.

The combined gas law is easily derived from the ideal gas equation. Consider a confined gas, with a fixed number of moles, n, at different pressure, volume and temperature.

P1V1 = nRT1
P2V2 = nRT2

Solve each for nR since they are constants
nR = P1V1 / T1
nR = P2V2 / T2

Since two the two different expressions are both equal to nR, they are equal, and you have the combined gas law.
P1V1 / T1 = P2V2 / T2