How to find tangent line of this equation

it says estimate the slope of the line tangent to each function at given point. At which point is it not possible to draw a tangent line?
f(x)= X+3/x-3 where x=4
how do you do questions like this? step by step please :S
the answer is -6; x=3
i tried using the rate of change eqation didnt work for me helpp!!

first calculate its derivative and then put x=4 in it. this is how you can find slope of tangent at a given point

let y=x+3/x-3
by taking derivative w. r. t x
dy/dx= d/dx{x+3/x-3}
dy/dx={(x-3) d/dx(x+3)-(x+3)d/dx(x-3)}/(x-3)^2 quotient rule
dy/dx={(x-3)(1)-(x+3)(1)}/(x-3)^2
={x-3-x-3}/(x-3)^2
=-6/(x-3)^2
this is the derivative now put x=4 in it to find out slope of tangent at x=4
slope=-6/(4-3)^2
=-6
hope it helps