Quotient of Homogeneous Functions

Theorem
Let $$M \left({x, y}\right)$$ and $$N \left({x, y}\right)$$ be homogeneous functions of the same degree.

Then:
 * $$\frac {M \left({x, y}\right)} {N \left({x, y}\right)}$$

is homogeneous of degree zero.

Proof
Let:
 * $$Q \left({x, y}\right) = \frac {M \left({x, y}\right)} {N \left({x, y}\right)}$$

where $$M$$ and $$N$$ are homogeneous functions of degree $$n$$.

Let $$t \in \R$$. Then:

$$ $$ $$ $$ $$

The result follows from the definition.