Substitutions in multiple integrals

R is a region in the first quadrant of the xy-plane bounded by xy=1, xy=9, y=x, and y=3x. Using the transformation $\displaystyle v=\sqrt{\frac{y}{x}}$, $\displaystyle u=\sqrt{xy}$ with u>0, v>0 to rewrite the integral below over an appropriate region G in the uv-plane. Then evaluate the uv-integral over G.

$\displaystyle \displaystyle \int\int_{R}(\sqrt{\frac{y}{x}}+\sqrt{xy})dxdy$

I'm totally lost on this. This is an exam review question but for all of our examples in the textbook the transformation is written in terms of x=... and y=...

I have no idea what to do here.