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Why ratio in external division is negative?

I have answer for how it is negative but not why?

X = (mx2+nx1)/(m+n)

⇒ (mx2+nx1) = X(m+n)

⇒m(x2-X) = n(X-x1)

⇒(m/n) = (X-x1)/(x2-X)

From the above equation we can conclude that when division is external then X must be greater than x1 and x2, therefore ratio becomes negative

But whats the purpose of negative ratio.