How do I reduce this fraction: y/x+x/y / 1/xy

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How do I reduce this fraction: y/x+x/y / 1/xy

Mathematics
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combine fractions in numerator y/x + x/y = (y^2+x^2)/xy multiply by reciprocal of denominator (y^2+x^2)/xy * xy/1 = y^2 + x^2
\[\frac{\frac{y}{x}+\frac{x}{y}}{\frac{1}{x y}}=\frac{\frac{x^2+y^2}{x y}}{\frac{1}{x y}}=x^2+y^2 \]
yeah that looks better

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Other answers:

Hey guys, I'm new here. How did robtobey write that? The Equation editor has no fractions???
i wish i knew too
This is a test {2}{3}
This is a test frac{2}{3}
This is a test \frac{2}{3}
This is a test [\frac{2}{3}]
Mathematic 8 will copy and paste LaTex. it is done in two steps. First right click on the Mathematica expression. Then holding down the right click button, slide down to the Copy As which puts up a secondary window offering Copy As LaTex or MathML. Considering the technology embedded in this program and the years of development, they essentially give it away to students and teachers.
\[\frac{\frac{3}{y}}{\frac{2}{x}+1}\]
Thank you robtobey. I will read this and look into it...
I don't have Mathemataica at our college.
I'm clicking on Equation editor and using the LaTeX frac{a}{b} command.
I can learn the LaTeX commands on an as-needed basis, as I go along.
\[\dfrac{x}{y}\]

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