Práctica 0 ejercicio 1g - versión 2017

EJERCICIO 1: Calcule

(g) $ \left( \dfrac{4}{3} - \dfrac{2}{9}\right)^{-1} \left( \dfrac{5}{6} + \dfrac{1}{2}\right)^{2} $

Solución:

\begin{eqnarray*}
\left( \dfrac{4}{3} - \dfrac{2}{9}\right)^{-1} \left( \dfrac{5}{6} + \dfrac{1}{2}\right)^{2} & = & \left( \dfrac{12-2}{9}\right)^{-1} \left( \dfrac{5+3}{6} \right)^{2} \\
& = & \left( \dfrac{10}{9}\right)^{-1} \left( \dfrac{8}{6} \right)^{2} \\
& = & \left( \dfrac{10}{9}\right)^{-1} \left( \dfrac{4}{3} \right)^{2} \\
& = & \dfrac{9}{10} \cdot \dfrac{4^{2}}{3^{2}} \\
& = & \dfrac{\cancel{9}}{10} \cdot \dfrac{16}{\cancel{9}} \\
& = & \dfrac{16}{10} \\
& = & \dfrac{8}{5} \\

\end{eqnarray*}

$$\boxed{ \left( \dfrac{4}{3} - \dfrac{2}{9}\right)^{-1} \left( \dfrac{5}{6} + \dfrac{1}{2}\right)^{2} = \dfrac{8}{5} }$$