You CAN just beat the tar out of it...
1) Multiply out the LHS.
2) Subtract the 2xyz
3) Divide by xyz
4) Rearrange so that reciprocals are grouped together.
5) Ponder the reciprocal pairs.
6) Prove that any reciprocal pair >= 2
f(A) = A + 1/A
What can you tell of that? Maybe a graph would be helpful?
Nothing like a little algebra practrice.