If a line parallel to X axis but not identical with X axis cuts the graph of the curve y= x-1/(x-2)(x-3) at x=a,x=b only, then evaluate (a-1) (b-1).

equation of line is y=k,then, x-1=k(x²-5x+6), kx² -(5k+1)x+6k+1=0

(a-1)(b-1) =ab-(a+b)+1=6+(1/k)+5+(1/k)+1=12+(2/k)

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