Question

Simplifique a expressão abaixo:

$\mathsf{\left(\dfrac{\left(\dfrac{5}{6}\right)^2+2\cdot\left(\dfrac{1}{18}\right)\cdot\left(\dfrac{1}{6}\right)-\left(\dfrac{2}{5}\right)^2}{\sqrt{\left(\dfrac{3}{5}+\dfrac{4}{3}\right)^2}}\right)=\,?}$
​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\left(\dfrac{\left(\dfrac{5}{6}\right)^2 + 2\:.\:\left(\dfrac{1}{18}\right)\:.\:\left(\dfrac{1}{6}\right) - \left(\dfrac{2}{5}\right)^2}{\sqrt{\left(\dfrac{3}{5} + \dfrac{4}{3}\right)^2}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{25}{36} + \dfrac{2}{108} - \dfrac{4}{25}}{\sqrt{\left(\dfrac{3}{5} + \dfrac{4}{3}\right)^2}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{25}{36} + \dfrac{2}{108} - \dfrac{4}{25}}{\sqrt{\left(\dfrac{9 + 20}{15}\right)^2}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{25}{36} + \dfrac{2}{108} - \dfrac{4}{25}}{\dfrac{29}{15}}\right)}$

$\mathsf{\left(\dfrac{\dfrac{1875 + 50 - 432}{2700}}{\dfrac{29}{15}}\right)}$

$\mathsf{\dfrac{1493}{2700}\:.\:\dfrac{15}{29}}$

$\mathsf{\dfrac{22395 \div 15}{78300 \div 15}}$

$\mathsf{\left(\dfrac{\left(\dfrac{5}{6}\right)^2 + 2\:.\:\left(\dfrac{1}{18}\right)\:.\:\left(\dfrac{1}{6}\right) - \left(\dfrac{2}{5}\right)^2}{\sqrt{\left(\dfrac{3}{5} + \dfrac{4}{3}\right)^2}}\right) = \dfrac{1493}{5220}}$

Answer 2

Hi !

Resolução

Para resolver essa questão primeiramente nós temos que resolver tudo que está dentre os parênteses, depois as potências, frações, multiplicações e por último as demais contas:

Resolvendo

$\sf \displaystyle \left(\frac{\left(\dfrac{5}{6}\right)^2+2\cdot \left(\dfrac{1}{18}\right)\cdot \left(\dfrac{1}{6}\right)-\left(\dfrac{2}{5}\right)^2}{\sqrt{\left(\dfrac{3}{5}+\frac{4}{3}\right)}^2}\right)\\\\\\\sf =\frac{\left(\dfrac{5}{6}\right)^2+2\cdot \dfrac{1}{18}\cdot \dfrac{1}{6}-\left(\dfrac{2}{5}\right)^2}{\left(\sqrt{\dfrac{3}{5}+\dfrac{4}{3}}\right)^2}\\\\\\\sf =\dfrac{\dfrac{1493}{2700}}{\left(\sqrt{\dfrac{3}{5}+\dfrac{4}{3}}\right)^2}$

$\sf =\dfrac{\dfrac{1493}{2700}}{\dfrac{29}{15}}\\\\\\\sf =\dfrac{1493\cdot \:15}{2700\cdot \:29}\\\\\\\sf \boxed{\sf \frac{1493}{5220}}$

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