Are positive rational numbers x and y, for which number

$\displaystyle \frac {x+\sqrt{y}}{y+\sqrt{x}}=Q$

is rational. Prove that both x and y are squares of rational numbers.

what I did:

$\displaystyle a= \sqrt{x}$

$\displaystyle b= \sqrt{y}$

$\displaystyle \frac{a ^{2}+b}{b^{2}+a}=\frac{a ^{2}+b}{b^{2}+a}* \frac{b^{2}-a}{b^{2}-a}= \frac{a^{2}b^{2}-a^{3}+b^{3}-ab}{b^{4}-a^{2}}$

I don't know what to do next ;<