$\begin{align} & \left[ a\div \left( b\div c \right) \right]\div \left[ \left( a\div b \right)\div c \right]=\left( a\div \left( \frac{b}{c} \right) \right)\div \left( \left( \frac{a}{c} \right)\div c \right)= \\ & \left( a\times \frac{c}{a} \right)\div \left( \left( \frac{a}{b} \right)\times \left( \frac{1}{c} \right) \right)=\left( \frac{ac}{b} \right)\times \left( \frac{bc}{a} \right)={{c}^{2}} \\ \end{align}$