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Let y = (x - 3)/(x + 1). The equation can be expressed in the form (x+a)(y+b)=c. Find a, b, c.

Jun 14, 2021

We have $y = \frac{x - 3}{x + 1} = 1 - \frac{4}{x+1}$.  So $\frac{4}{x+1} = 1-y$.  Since $x\ne -1$ we can multiply $x+1$ to both sides to get $(x+1)(1-y)=4$, or equivalently, $(x+1)(y-1)=-4$, i.e., $a=1$, $b=-1$ and $c=-4$.