Why does dividing one odd function by another give an even function?

[hyper]

Why does two odd functions divided by each other become an even function?

 

[Defennder]

Well suppose you have 2 odd functions f(x) and g(x). Since they are odd, f(x)= -f(-x) and similarly for g(x). Now divide f(x) by g(x) on both sides of the equation. What do you observe?

 

[HallsofIvy]

[tex]\frac{f}{g}(-x)= \frac{f(-x)}{g(-x)}= \frac{-f(x)}{-g(x)}= \frac{f(x)}{g(x)}= \frac{f}{g}(x)[/itex][/tex]

 

[hyper]

thanks!