Dividing Rational Expressions
posted by Jaz on .
x^38/x^24 divided by (x^2+2x+4)/(x^3+8). This becomes ((x2)(x^2+2x+4)/(x+2)(x2) times ((x+2)(x^22x+4))/(x^2+2x+4). I understand that (x2)(x^2+2x+4)=(x^38) when I distribute it, however, if I didn't have the help of my book, I'd have no clue how to come up with this on my own. Is there a general rule for how to distribute x's to the third power? Thank you!!

yes!
We can factor both the sum and the difference of cubes
A^3 + b^3 = (A+B)(A^2  AB + B^2) and
A^3  b^3 = (AB)(A^2 + AB + B^2)
that is where those factors came from.
Most of the stuff canceled and you should have had x^2  2x + 4 as the answer.