We need to find the equation of a tangent line, and to do that you need to find derivative to be able to complete the equation.

So, it gives y= (x-1)/(x-2) on coordinate (3,2)

I say:

a=3

f(a)=2

f`(3)= ?

Usinglim h-->0 f(a+h)-f(a) / hto find f`(3)

I plug in [(3+h-1)/(3+h-2) -2] / h

=(3+h-1)-2(3+h-2) / h(3+h-2) (After multiplying by CD)

=3+h-1-6-2h+4 / 3h+h^2-2h

=-2 / 2h+h-2

=-2/-2

=1

The book is showing the derivative as-1. Where did I mess up here?