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

I also got E. What's the OA?