296. La expresión $\left[ \left( \frac{1}{2}-\frac{1}{3} \right)\cdot \left( \frac{5}{6}-\frac{7}{12} \right) \right]:\frac{1}{24}$ es igual a

a) ${}^{5}\!\!\diagup\!\!{}_{12}\;$

b) 1

c) ${}^{7}\!\!\diagup\!\!{}_{24}\;$

Operando:

$\left[ \left( \frac{1}{2}-\frac{1}{3} \right)\cdot \left( \frac{5}{6}-\frac{7}{12} \right) \right]:\frac{1}{24}\quad =$

$=\quad \left[ \left( \frac{1\times 3}{2\times 3}-\frac{1\times 2}{3\times 2} \right)\cdot \left( \frac{5\times 2}{6\times 2}-\frac{7}{12} \right) \right]:\frac{1}{24}\quad =$

$=\quad \left[ \left( \frac{3}{6}-\frac{2}{6} \right)\cdot \left( \frac{10}{12}-\frac{7}{12} \right) \right]:\frac{1}{24}\quad =$

$=\quad \left[ \left( \frac{3-2}{6} \right)\cdot \left( \frac{10-7}{12} \right) \right]:\frac{1}{24}\quad =\left[ \left( \frac{1}{6} \right)\cdot \left( \frac{3}{12} \right) \right]:\frac{1}{24}\quad =$

\[=\left[ \left( \frac{1}{6} \right)\times \left( \frac{3}{12} \right) \right]\times \frac{24}{1}\quad =\frac{1\times 3\times 24}{6\times 12\times 1}\quad =\]

\[=\ \ \frac{\not{3}\times \not{4}\times \not{6}}{\not{6}\times \not{3}\times \not{4}}\quad =\ \ 1\]