KöMaL 2006 C845

In an algebra class on the first of April, the students were practising. The task was to simplify the fraction $\frac{{(x+2)}^3+{(y+x)}^3}{{(x+2)}^3-{(y-2)}^3}.$ Agnes, who was the best at mathematics in the class, suggested that if the denominator is not zero, they should just cross out the threes in all the indices, that is, write $\frac{x+2+y+x}{x+2-(y-2)}= \frac{2x+y+2}{x-y+4}.$ Check the result.