I'm told that the following two equations are equal, and asked to write the steps to manipulate the first equation into the second.

$\displaystyle 1 - \frac{1}{k + 1} + \frac{1}{(k+1)(k+2)}$

to

$\displaystyle 1 - \frac{1}{k + 1}\bigg[1 - \frac{1}{(k+2)}\bigg]$

I've tried many different ways of writing the first equation, but I can't seem to get it to work. Could someone point me in the right direction?