#### Answer

$f'(3)=\frac{-1}{4}$

#### Work Step by Step

To find the slope of a function at any given point, all one has to do would be to look for the value of the derivative function at the same x value.
Given that $f(x)=\frac{1}{x-1}={(x-1)}^{-1}$, then the derivative function by the power rule will be $f'(x)=(-1)(x-1)^{-1-1}=-(x-1)^{-2}=\frac{-1}{(x-1)^2}$
As such, the slope at the point $x=3$ would be $f'(3)=\frac{-1}{(3-1)^2}=\frac{-1}{4}$