distributive property of division over subtraction

Distributive property of division over subtraction:We know distribution means dividing one element to multiple element. Hence distributing property means if we multiply two set of number, like two elements in bracket and one outside the bracket, then the result will  be same as the multiplication of individual elements. As example, [tex]x\times(y+z) = x\timesy + x\times z[/tex]So generally it works on multiplication over addition, and directly do not work on division over subtraction. But division over subtraction can work only in case of reciprocals as division is opposite of multiplication and subtraction can be done by adding one positive and one negative numbers. Example, [tex]\frac{(x-y)}{z} = \frac{(x+(-y))}{y} = \frac{x}{z} =\frac{x}{z}-\frac{y}{z}[/tex]But [tex]\frac{z}{(x-y)}[/tex] case will not work.