This section doesn't actually have many to do with the rest of this chapter, but since the subject required to be covered and it was a fairly short chapter it appeared like as good a place as any to put it.
Hence, let's begin with the following. Let's assume that we desire to add the following two rational expressions.
8/(x+1) -5/(x-4) = 8 ( x - 4)/(x+1)(x+4) -5(x+1)/ (x+1)(x+4)
= 8x -32- (5x+5)/(x+1)(x-4)
= 3x-37/(x+1)(x-4)