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

EunoR 2021-09-28 Answered
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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dessinemoie
Answered 2021-09-29 Author has 21722 answers
\(\displaystyle{\frac{{{\left(\frac{{5}}{{x}^{{{2}}}}\right)}-{\left(\frac{{3}}{{x}}\right)}}}{{{\left(\frac{{1}}{{y}}\right)}+{\left(\frac{{2}}{{y}^{{{2}}}}\right)}}}}={\frac{{{\frac{{{5}{x}-{3}}}{{{x}^{{{2}}}}}}}}{{{\frac{{{y}+{2}}}{{{y}^{{{2}}}}}}}}}\)
\(\displaystyle={\frac{{{5}{x}-{3}}}{{{x}^{{{2}}}}}}\times{\frac{{{y}^{{{2}}}}}{{{y}+{2}}}}\)
\(\displaystyle={\frac{{{5}{x}{y}^{{{2}}}-{3}{y}^{{{2}}}}}{{{x}^{{{2}}}{y}+{2}{x}^{{{2}}}}}}\)
\(\displaystyle{\frac{{{\left(\frac{{5}}{{x}^{{{2}}}}\right)}-{\left(\frac{{3}}{{x}}\right)}}}{{{\left(\frac{{1}}{{y}}\right)}+{\left(\frac{{2}}{{y}^{{{2}}}}\right)}}}}={\frac{{{5}{x}^{{{2}}}-{3}{y}^{{{2}}}}}{{{x}^{{{2}}}{y}+{2}{x}^{{{2}}}}}}\)
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