From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
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 in the numerator, and we also need a positive 3 in 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 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.