# express in simplest form

• Sep 18th 2009, 12:58 PM
express in simplest form
2/x^2 + 2/y^2
---------------
4/xy
• Sep 18th 2009, 01:10 PM
e^(i*pi)
Quote:

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

You can use latex to make your question easier to understand, Click on my representation of the question.

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

Cross multiply to give just one denominator

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

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

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

$\displaystyle xy$ will cancel as will $\displaystyle 2$

$\displaystyle \frac{x^2+y^2}{2xy}$
• Sep 18th 2009, 01:13 PM
Plato
Quote:

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