2007 H2 Mathematics

Show that the equation $y=\frac{2x+7}{x+2}$ can be rewritten as $y=A+\frac{B}{x+2},$ where $A$ and $B$ are constants to be found.

Hence state a sequence of transformations which transform the graph of $y=\frac{1}{x}$ to the graph of $y=\frac{2x+7}{x+2}.$

Sketch the graph of $y=\frac{2x+7}{x+2},$ giving the equations of any asymptotes and the coordinates of any points of intersection with the $x\text{-}$ and $y\text{-axes}.$