Question

Resolver a seguinte expressão:
$~$
$\mathsf{\left[\left(\dfrac{2}{3}-\dfrac{1}{6}\left)^2+\dfrac{1}{2}\right]~:~\left(\dfrac{3}{4}+\dfrac{1}{2}-1\right)}$​

Answer 1

Resposta:

$3$

Explicação passo a passo:

Primeiro, precisamos resolver as expressões dentro dos parênteses. Temos:

$\left[\left(\dfrac{2}{3}-\dfrac{1}{6}\right)^2+\dfrac{1}{2}\right]:\left(\dfrac{3}{4}+\dfrac{1}{2}-1\right) \\ \\ =\left[\left(\dfrac{2\cdot2-1\cdot1}{6}\right)^2+\dfrac{1}{2}\right]:\left(\dfrac{3\cdot1+1\cdot2-1\cdot4}{4}\right) \\ \\ =\left[\left(\dfrac{4-1}{6}\right)^2+\dfrac{1}{2}\right]:\left(\dfrac{3+2-4}{4}\right) \\ \\ =\left[\left(\dfrac{3}{6}\right)^2+\dfrac{1}{2}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\left(\dfrac{1}{2}\right)^2+\dfrac{1}{2}\right]:\left(\dfrac{1}{4}\right)$

$=\left[\dfrac{1^2}{2^2}+\dfrac{1}{2}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\dfrac{1}{4}+\dfrac{1}{2}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\dfrac{1\cdot1+1\cdot2}{4}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\dfrac{1+2}{4}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\dfrac{3}{4}\right]:\left(\dfrac{1}{4}\right) \\ \\ =\left[\dfrac{3}{4}\right]\cdot\left(\dfrac{4}{1}\right)=\dfrac{3\cdot4}{4\cdot1} \\ \\ =\dfrac{3}{1}=3$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{\left[\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2 + \dfrac{1}{2}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\left(\dfrac{4 - 1}{6}\right)^2 + \dfrac{1}{2}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\left(\dfrac{3}{6}\right)^2 + \dfrac{1}{2}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\left(\dfrac{1}{2}\right)^2 + \dfrac{1}{2}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\dfrac{1}{4} + \dfrac{1}{2}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\dfrac{1 + 2}{4}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\dfrac{3}{4}\right]\::\:\left(\dfrac{3}{4} + \dfrac{1}{2} - 1\right)}$

$\sf{\left[\dfrac{3}{4}\right]\::\:\left(\dfrac{3 + 2 - 4}{4}\right)}$

$\sf{\left[\dfrac{3}{4}\right]\::\:\left[\dfrac{1}{4}\right]}$

$\sf{\left[\dfrac{3}{4}\right]\:\times\:\left[\dfrac{4}{1}\right] = \dfrac{12}{4}}$

$\boxed{\boxed{\boxed{\sf{3}}}}$