What rule is this and please explain it

I notice in various problems (x/n)-(y/z)
=(zx-ny)/(n)(z)
I never learned this in my algebra class. How does this come out equally?

Im sure youve learned it even thuogh you dont kknow it. Its basic algebra is al - we are adding two rational expressions by giving them both the same denoominator.

x/n - y/z

xz/nz - y/z
xz/nz - yn/nz
(xz- yn)/ nz

This is not some special identity you need to memorize.

It's called a common denominator, or combining fractions with different denominators.

Assuming n and z are nonzero,

x/n = xz/nz
y/z = yn/zn
zn = nz

x/n - y/z = (xz - yn)/zn

To solve this, you need to put everything under a common denominator, which in this case is "nz".
So you get:
(xz/zn) - ( ny/zn)=
xz-ny/zn=