Prove that if each of x, y, and z is a number, and neither y nor z is 0, then y*z does not equal 0, and (x*z)/(y*z) = x/y.
If z is not 0, then z has a multiplicative inverse, $\displaystyle z^{-1}$. For the first part, multiply both sides of yz= 0 by $\displaystyle z^{-1}$ to get a contradiction. For the second multiply numerator and denominator of (xz)/(yz) by $\displaystyle z^{-1}$.