Function y = x/(x-1) is self-inverse: x = y/(y-1) (symmetric on first diagonal y=x).

It is the function giving the ratio y = XA/XB for a point on line AB described parametrically through.

X = (1-x)A + xB.

Then the ratio.

y = XA/XB = x/(x-1).

The graph of the function describes a rectangular hyperbola. The red points are the foci of the hyperbola.

Point (1,1) is its center and x = 1, y = 1 are its asymptotic lines.

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