# Simplify each of the complex fractions. \frac{(5/x^{2})-(3/x)}{(1/y)+(2/y^{2}

Simplify each of the complex fractions. $$\displaystyle{\frac{{{\left(\frac{{5}}{{x}^{{{2}}}}\right)}-{\left(\frac{{3}}{{x}}\right)}}}{{{\left(\frac{{1}}{{y}}\right)}+{\left(\frac{{2}}{{y}^{{{2}}}}\right)}}}}$$.

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$$\displaystyle{\frac{{{\left(\frac{{5}}{{x}^{{{2}}}}\right)}-{\left(\frac{{3}}{{x}}\right)}}}{{{\left(\frac{{1}}{{y}}\right)}+{\left(\frac{{2}}{{y}^{{{2}}}}\right)}}}}={\frac{{{\frac{{{5}{x}-{3}}}{{{x}^{{{2}}}}}}}}{{{\frac{{{y}+{2}}}{{{y}^{{{2}}}}}}}}}$$
$$\displaystyle={\frac{{{5}{x}-{3}}}{{{x}^{{{2}}}}}}\times{\frac{{{y}^{{{2}}}}}{{{y}+{2}}}}$$
$$\displaystyle={\frac{{{5}{x}{y}^{{{2}}}-{3}{y}^{{{2}}}}}{{{x}^{{{2}}}{y}+{2}{x}^{{{2}}}}}}$$
$$\displaystyle{\frac{{{\left(\frac{{5}}{{x}^{{{2}}}}\right)}-{\left(\frac{{3}}{{x}}\right)}}}{{{\left(\frac{{1}}{{y}}\right)}+{\left(\frac{{2}}{{y}^{{{2}}}}\right)}}}}={\frac{{{5}{x}^{{{2}}}-{3}{y}^{{{2}}}}}{{{x}^{{{2}}}{y}+{2}{x}^{{{2}}}}}}$$