r4e said it how i would have put it if i tried to tell you.
You could think of it another way though (albeit, similar to r4e method)
Given xyz=0 (sorry, for any sort of algebraic maneuver you need two sides to an equation, 0 in this case so nothing gets done on the RHS).
To get x, we can take steps through y and z separately, so that xz=0 (by diving by y first, you know this is what you get), then dividing by z, you get x=0. What you've essentially done though, is multiplied xyz by 1/y and then by 1/z, and since multiplication is associative (thats the technical jargain), (xyz * 1/y)*1/z = xyz*(1/y * 1/z) = xyz*(1/yz) = xyz/(yz) = x.
I like maths, maths is fun fun fun