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 -x2 into the numerator, and we need a positive 3 into the numerator. Better clear some room, boys.
To get the -x2 into the numerator, add the clever form of 0 (-x2 + x2):
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 x2 + 4x – 5 is less than the degree of x3 – x2 + 3, we're done. 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.