6x+9/x-5 x is not equal to 5 find inverse

You have f(x)=(6x+9)/(x-5) and want to find the inverse function?  Please note that the parentheses are obligatory here.

1.  Replace "f(x)" with y:   y = (6x+9)/(x-5)

2.  Interchange the variables x and y:     x = (6y+9)/(y-5)

3.  Solve this result for y:     x(y-5) = (6y+9), or xy-5x = 6y+9.  Then:
                                                             
                                            xy-6y = 9 + 5x, or y(x-6) = 9+5x
                                                             9+5x
                     Then                      y =                       
                                                             x-6

Here x may not = 6, because division by zero would occur otherwise.