There's a good bit of trickery needed here. You might want to call on Loki or whatever other gods of mischief you've got in your back pocket for some assistance. We need a -x^{2} in the numerator, and we also need a positive 3 in the numerator. Better clear some room, boys.

To get the -x^{2} into the numerator, add the clever form of 0 (-x^{2} + x^{2}):

To get 3 into the numerator, add another clever form of 0 (3 – 3):

Now we can split up the fraction into two parts. The second part probably won't be as good as the first part, because the sequel always seems to take a step backward.

Since the degree of x^{2} + 4x – 5 is less than the degree of x^{3} – x^{2} + 3, we can turn that first fraction into a 1 and keep the second one as-is. Thank you, thank you, we'll be here all night. Actually, we won't. In fact, we need to wake up kind of early tomorrow.