Pulling out -1 from denominator?

[bob1182006]

I know this might seem trivial but I've never had a teacher cover this even though I've had the whole "factor out -1 from numerator " class.

I was thinking of the cases but I haven't found a contradiction to:

$$\frac{a}{b-c}=-1\frac{a}{c-b}$$

so is this always true?

 

[DeadWolfe]

Obviously. After all (-x)/y=x/(-y)=-(x/y).

 

[CRGreathouse]

It's true. It's a special case of

$$\frac{1}{ab}=\frac1a\cdot\frac1b$$

 

[bob1182006]

thanks
I've always wondered about that...
for some reason no teacher I've had has ever done that manipulation.

 

[arildno]

You might try to prove the following statements:
$$\frac{1}{1}=1, \frac{1}{(-1)}=(-1)*\frac{1}{1}=(-1)$$