Find the equation of the tangent to the curve

y = (x - 7)/{(x-2)(x-3)} at the point where it cuts the x - axis.

Dear

y= (x - 7)/{(x-2)(x-3)}

for sut point on x axis put y=0

 x=7 

so point is (7,0)

now

 dy/dx =  [(x-2)(x-3)  - (x-7)(2x-5)]/{(x-2)(x-3)}²

             = 1/20    at (7,0)

so euation of tangent

y-0 = 1/20 (x-7)

 x-20y -7=0

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