His overall net profit would be $500 dollars because every two weeks he makes $500 so over 4 weeks he would make $1000, but lose $500 to rent.
When
, you're left with
When
or
, you're left with
Adding the two equations together gives
, or
. Subtracting them gives
,
.
Now, you have
By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that
and
. These alone tell you that you must have
and
.
So the partial fraction decomposition is