What are the rules to simplify this equation?

Question

I know that I can these two terms are equal, but I would like to understand why the are equal and what rules are involved in translating one term in the other. Here are the terms: $$-\frac{ae^{-ax}}{1 + e^{-ax}} = -\frac{a}{1 + e^{ax}}$$

Thank you very much!

Answer 1

Hint: Write

$$-\frac{ae^{-ax}}{1+e^{-ax}}\cdot \frac{e^{ax}}{e^{ax}}$$

Answer 2

Hint: Try cross-multiplying. Then simplify each side.