# Exponent of Sum/Real Numbers/Corollary

## Corollary to Exponent of Sum: Real Numbers

Let $x, y \in \R$ be real numbers.

Let $\exp x$ be the exponential of $x$.

Then:

- $\exp \left({x - y}\right) = \dfrac {\exp x} {\exp y}$

## Proof

By Exponent of Sum: Real Numbers:

- $\exp \left({x - y}\right) = \exp x \exp \left({- y}\right)$

By Reciprocal of Complex Exponential:

- $\dfrac 1 {\exp y} = \exp \left({- y}\right)$

Combining these two, we obtain the result:

- $\exp \left({x - y}\right) = \dfrac {\exp x} {\exp y}$

$\blacksquare$