If \( a, b, c \) are all different and the points \( \left(\frac{r^{3}}{r-1}, \frac{r^{2}-3}{r-1...

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If \( a, b, c \) are all different and the points \( \left(\frac{r^{3}}{r-1}, \frac{r^{2}-3}{r-1}\right) \) where \( r=a, b, c \) are collinear, then prove that \( 3(a+b+c)=a b+ \) \( b c+c a-a b c \).
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