# Why does $\frac{a-x}{x-a} = -1$

Why does $$\frac{a-x}{x-a}$$ simplify to $$-1$$?

I have no idea where to start because there are multiple minus signs involved.

• I remember that for some reason this was mindblowing to me when I first learned fractions – Spine Feast Dec 23 '14 at 13:11

Hint: $$\frac{a-x}{x-a}=\frac{-(x-a)}{x-a}=\ldots$$ Of course, for this to make sense the denominator shouldn't be equal to $0$, hence $x$ must not be equal to $a$. Otherwise it would be undefined.

• fastest answer I've ever seen, haha. Thanks. – user1534664 Dec 23 '14 at 13:07
• @user1534664 You're welcome ;) – Workaholic Dec 23 '14 at 13:08

The correct way to simplify this is to say that $\frac{a-x}{x-a}=-1$ if $x\ne a$ and undefined if $x=a$.