Is the answer E - 9? The way I solved this was to make a substitution...if we make new variables, say r and s such that
r = sqrt(x)
s = sqrt(y)
then we can substitute these and it's a little easier to see how the problem is solved. We can use r and s to write the equation as
(r + s)/(r^2 - s^2) = (2r + 2s)/(r^2 + 2rs + s^2)
then, we can factor both denominators and get
(r + s)/((r + s)(r - s)) = (2(r + s))/((r + s)^2)
Then, cancelling the (r+s) factors gives
1/(r-s) = 2/(r+s)
We can rearrange this to get
r + s = 2r - 2s
3s = r
3 = r/s
Then, remembering the substitution we made, we can plug back in sqrt(x) and sqrt(y)
3 = sqrt(x)/sqrt(y)
9 = x/y
