Finding the critical points of a function and the interval where it increases and decreases.

I am having trouble finding the critical points of

$f(x)=(x+1)/x-3$

I found the derivative to be ${f}^{\prime}(x)=-4/(x-3{)}^{2}$.

My next step was to equate my derivative to zero, but that does not seem to work as my x cancels out. Usually I would take the x-value(worked out by equating the derivative with zero) and substitute it into the original equation to get a y-value. This would then be the critical points. Is there anyone who could maybe help me out (maybe with an example or so) as I also have to find the intervals where the function is increasing and decreasing?

I am having trouble finding the critical points of

$f(x)=(x+1)/x-3$

I found the derivative to be ${f}^{\prime}(x)=-4/(x-3{)}^{2}$.

My next step was to equate my derivative to zero, but that does not seem to work as my x cancels out. Usually I would take the x-value(worked out by equating the derivative with zero) and substitute it into the original equation to get a y-value. This would then be the critical points. Is there anyone who could maybe help me out (maybe with an example or so) as I also have to find the intervals where the function is increasing and decreasing?