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

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

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    $\begingroup$ I remember that for some reason this was mindblowing to me when I first learned fractions $\endgroup$ Dec 23, 2014 at 13:11

2 Answers 2

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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.

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    $\begingroup$ fastest answer I've ever seen, haha. Thanks. $\endgroup$ Dec 23, 2014 at 13:07
  • $\begingroup$ @user1534664 You're welcome ;) $\endgroup$
    – Workaholic
    Dec 23, 2014 at 13:08
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The correct way to simplify this is to say that $\frac{a-x}{x-a}=-1$ if $x\ne a$ and undefined if $x=a$.

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