426. La expresión $\left[ \left( \frac{1}{2}-\frac{3}{4} \right)\cdot \left( \frac{1}{6}+\frac{3}{2} \right) \right]:\frac{-5}{12}$ es igual a

a) 1

b) ${}^{-25}\!\!\diagup\!\!{}_{144}\;$

c) -1

 

Operando:

 

$\left[ \left( \frac{1}{2}-\frac{3}{4} \right)\cdot \left( \frac{1}{6}+\frac{3}{2} \right) \right]:\frac{-5}{12}\quad =$

 

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

 

$=\quad \left[ \left( \frac{2}{4}-\frac{3}{4} \right)\cdot \left( \frac{1}{6}+\frac{9}{6} \right) \right]:\frac{-5}{12}\quad =$

 

$=\quad \left[ \left( \frac{2-3}{4} \right)\cdot \left( \frac{1+9}{6} \right) \right]:\frac{-5}{12}\quad =\left[ \left( \frac{-1}{4} \right)\cdot \left( \frac{10}{6} \right) \right]:\frac{-5}{12}\quad =$

 

\[=\left[ \left( \frac{-1}{4} \right)\times \left( \frac{10}{6} \right) \right]\times \frac{12}{-5}\quad =\frac{\left( -1 \right)\times 10\times 12}{4\times 6\times \left( -5 \right)}\quad =\]

 

\[=\ \ \frac{-\not{2}\times \not{5}\times \not{2}\times \not{6}}{-\not{2}\times \not{2}\times \not{6}\times \not{5}}\quad =\ \ 1\]