Sketch the graph of the function $f(x)=ln(\frac{x+1}{x-2}).$

$($a$)$ Find the domain of the function and intercepts with axis:

$($b$)$ Find the asymptotes if any:

$($c$)$ Determine that the function is increasing or decreasing:

$($d$)$ Determine that the function is concave up or concave down $($convex or concave$)$:

$($e$)$ Sketch the graph: