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.