# Math Help - express in simplest form

1. ## express in simplest form

2/x^2 + 2/y^2
---------------
4/xy

2/x^2 + 2/y^2
---------------
4/xy
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$\frac{\frac{2}{x^2} + \frac{2}{y^2}}{\frac{4}{xy}}$

Cross multiply to give just one denominator

Spoiler:
$\frac{2}{x^2}+\frac{2}{y^2} = \frac{2(y^2+x^2)}{x^2y^2}$

Remember when multiplying by fractions that $\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}$. In other words flip the fraction and multiply.

Spoiler:
$\frac{2(y^2+x^2)}{x^2y^2} \times \frac{xy}{4}$

$xy$ will cancel as will $2$

$\frac{x^2+y^2}{2xy}$

2/x^2 + 2/y^2
---------------
4/xy
$\displaystyle{\frac{{\frac{2}
{{x^2 }} - \frac{2}
{{y^2 }}}}
{{\frac{4}
{{xy}}}}} = {\frac{{\left( {\frac{2}
{{x^2 }} - \frac{2}
{{y^2 }}} \right)x^2 y^2 }}
{{\left( {\frac{4}
{{xy}}} \right)x^2 y^2 }}}$