Question

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} $

Answer 1

A common fraction is a fraction whose denominator is the same with another fraction.

$\sqrt{x} \div\sqrt{y}$ as a common fraction is $\sqrt \frac{x}{y}}$

The expression is given as:

$\sqrt{x} \div\sqrt{y}$

Express as fraction

$\sqrt{x} \div\sqrt{y} = \frac{\sqrt x}{\sqrt y}$

Rewrite as a common fraction

$\sqrt{x} \div\sqrt{y} = \sqrt \frac{x}{y}}$

Hence, $\sqrt{x} \div\sqrt{y}$ as a common fraction is $\sqrt \frac{x}{y}}$

Read more about common fractions at:

https://brainly.com/question/8672817