Question

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Answer 1

Ejercicios de Fracciones

[tex]\bold{{\left[\dfrac{3}{5}:\left( \dfrac{2}{4}+ \dfrac{5}{4}\right)+\dfrac{6}{5} }\right] x\sqrt[3]{\dfrac{125}{64} } }[/tex]

[tex]Resolvemos\ la \ raiz \cubica\\ \\ \\ \bold{\sqrt[3]{\dfrac{125}{64} }=\sqrt[3]{\dfrac{5^{3}}{4^{3} } }=\dfrac{\sqrt[3]{5^{3}}}{\sqrt[3]{4^{3}}} =\dfrac{\sqrt[\not3]{5^{\not3}}}{\sqrt[\not 3]{4^{\not 3}}} =\dfrac{5}{4} } \\ \\ \\ Entonces \\ \\ \\ \bold{{\left[\dfrac{3}{5}:\left( \dfrac{2}{4}+ \dfrac{5}{4}\right)+\dfrac{6}{5} }\right] x\sqrt[3]{\dfrac{125}{64} } =}[/tex]

[tex]\bold{{\left[\dfrac{3}{5}:\left( \dfrac{2}{4}+ \dfrac{5}{4}\right)+\dfrac{6}{5} }\right] x\dfrac{5}{4} } =}\qquad Resolvemos\ el\ parentesis\\ \\ \\ \bold{{\left[\dfrac{3}{5}:\left( \dfrac{2+5}{4}\right)+\dfrac{6}{5} }\right] x\dfrac{5}{4} } =}\\ \\ \\ \bold{{\left[\dfrac{3}{5}:\left( \dfrac{7}{4}\right)+\dfrac{6}{5} }\right] x\dfrac{5}{4} } =}\qquad Ahora \resolvemos\ la \ division \\ \\ \\ \bold{{\left[\dfrac{3*4}{5*7}+\dfrac{6}{5} }\right] x\dfrac{5}{4} } =}[/tex]

[tex]\bold{{\left[\dfrac{12}{35}+\dfrac{6}{5} }\right] x\dfrac{5}{4} } =}\qquad resolvemos \ la \ suma\\ \\ \\ \bold{{\left[\dfrac{12}{35}+\dfrac{6*7}{5*7} }\right] x\dfrac{5}{4} } =}\\ \\ \\ \bold{{\left[\dfrac{12}{35}+\dfrac{42}{35} }\right] x\dfrac{5}{4} } =}\\ \\ \\ \bold{{\left[\dfrac{12+42}{35}}\right] x\dfrac{5}{4} } =}\\ \\ \\ \bold{{\left[\dfrac{54}{35}}\right] x\dfrac{5}{4} } =\dfrac{54*5}{35*4}=\dfrac{270}{140} \ \ simplificamos\ =\dfrac{27}{14} }[/tex]

El resultado final es

[tex]\boxed{\bold{{\left[\dfrac{3}{5}:\left( \dfrac{2}{4}+ \dfrac{5}{4}\right)+\dfrac{6}{5} \right] x\sqrt[3]{\dfrac{125}{64} }=\dfrac{27}{14} }}}[/tex]

Espero que te sirva, salu2!!!!