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> If a divides b (a|b), this implies that there is some integer k such that ak = b.
>
> So since -1 divides 1, there must be some integer k such that -1 k = 1. We’ve established that this k value is 1/(-1).
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> In other words k = 1/(-1)
>
> which implies -1 = 1/k.
>
> 1/k = 1/(1/-1), or just -1.
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> Put more simply:
>
> The reason you accept (-1) cancels out, is because if you accept that a x 1/a, by definition of division and multiplication, you’re basically dividing a, a times, and saying it equals 1. in other words: -1 goes into 1, -1 times. QED
