Express \(\sqrt{x} \div\sqrt{y}\) as a common fraction given:
\(\frac{ {\left( \frac{1}{2} \right)}^2 + {\left( \frac{1}{3} \right)}^2 }{ {\left( \frac{1}{4} \right)}^2 + {\left( \frac{1}{5} \right)}^2} = \frac{13x}{41y}\)
First put the left side into its simplest form. Can you do that?
(you can use a calc if you have to but make sure it stays in fraction form)