Given, the equation of the tangent to the curve y = (x - 7)/{(x - 2)*(x - 3)} ...............1

Now, at the x-axis, y = 0

=> 0 = (x - 7)/{(x - 2)*(x - 3)}

=> x - 7 = 0

=> x = 7

So, the point is (7, 0)

Diferentiate equation 1 w.r.t. x, we get

dy/dx = {1 - y*(2x - 5)}/{(x -2)*(x - 3)}

Now dy/dx at (7, 0)

      dy/dx = {1 - 0*(2*7 - 5)}/{(7 -2)*(7 - 3)}

=> dy/dx = 1/(5*4)

=> dy/dx = = 1/20

So, the slope of the tangent = 1/20

Now, the eqyuation of tangent at (7, 0) is

      y - 0 = (1/20)*(x - 7)

=> y = (1/20)*(x - 7)

=> 20y = x - 7

=> x - 20y - 7 = 0

This is the required equation of the tangent.