Question

Ayuden con resoluciones plisss

Answer 1

Explicación paso a paso:

¡¡Hola un cordial saludo!!

Respuesta:

$\boxed{ \bold{ \huge{E = \frac{9}{2} }}}$

$\boxed{ \mathcal{NOTA:}}$

No daré mucha explicación debido a que el desarrollo del ejercicio es muy largo, espero me comprendas. Okey

Solucion:

$E = \frac{ \frac{6}{5}(1 + \frac{1}{6} )(1 + \frac{1}{7} )(1 + \frac{1}{8})(1 + \frac{1}{9} ) }{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7} )(1 - \frac{1}{8})(1 - \frac{1}{9} ) } \\ \\ E = \frac{ \frac{6}{5} \times \frac{7}{6} (1 + \frac{1}{7})(1 + \frac{1}{8} )(1 + \frac{1}{9} ) }{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7} )(1 - \frac{1}{8} )(1 - \frac{1}{9} )} \\ \\ E = \frac{ \frac{6}{5} \times \frac{7}{6} \times \frac{8}{7}(1 + \frac{1}{8})(1 + \frac{1}{9} ) }{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7})(1 - \frac{1}{8})(1 - \frac{1}{9} ) } \\ \\ E = \frac{ \frac{6}{5} \times \frac{7}{6} \times \frac{8}{7} \times \frac{9}{8} (1 + \frac{1}{9}) }{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7} ) (1 - \frac{1}{8})(1 - \frac{1}{9} ) } \\ \\ E = \frac{ \frac{6}{5} \times \frac{7}{6} \times \frac{8}{7} \times \frac{9}{8} \times \frac{10}{9} }{(1 - \frac{1}{5})(1 - \frac{1}{6})(1 - \frac{1}{7})(1 - \frac{1}{8} )(1 - \frac{1}{9} ) }$

Ahora cancelamos 9

$E = \frac{ \frac{5}{6} \times \frac{7}{6} \times \frac{8}{7} \times \frac{1}{8} \times 10}{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7} )(1 - \frac{1}{8} )(1 - \frac{1}{9}) }$

Cancelamos 8

$E = \frac{ \frac{6}{5} \times \frac{7}{6} \times \frac{1}{7} \times 10 }{(1 - \frac{1}{5})(1 - \frac{1}{6})( 1 - \frac{1}{7} )(1 - \frac{1}{8})(1 - \frac{1}{9} ) }$

Cancelamos 7 y 6.

$E = \frac{ \frac{1}{5} \times 10 }{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7} )(1 - \frac{1}{8})(1 - \frac{1}{9} ) }$

Multiplicamos 1/5 x 10.

$E = \frac{ \frac{10}{5} }{(1 - \frac{1}{5} )(1 - \frac{1}{6})(1 - \frac{1}{7} )(1 - \frac{1}{8})(1 - \frac{1}{9} )}$

Simplificamos 10/5 que es igual a 2.

$E = \frac{2}{(1 - \frac{1}{5})(1 - \frac{1}{6} )(1 - \frac{1}{7})(1 - \frac{1}{8} )(1 - \frac{1}{9} ) }$

Ahora seguimos desarrollando.

$E = \frac{ 2 }{ \frac{4}{5} (1 - \frac{1}{6} )(1 - \frac{1}{7} )(1 - \frac{1}{8} )(1 - \frac{1}{9} ) } \\ \\ E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} (1 - \frac{1}{7} )(1 - \frac{1}{8} )(1 - \frac{1}{9}) } \\ \\ E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7}(1 - \frac{1}{8} )(1 - \frac{1}{9}) } \\ \\ E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times \frac{7}{8} (1 - \frac{1}{9} )} \\ \\ E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} \times \frac{6}{5} \times \frac{6}{7} \times \frac{7}{8} \times \frac{8}{9} }$

Cancelamos 8, 7, 6 y 5.

$E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times 7 \times \frac{1}{9} } \\ \\ E = \frac{2}{ \frac{4}{5} \times \frac{5}{6} \times 6 \times \frac{1}{9} } \\ \\ E = \frac{2}{ \frac{4}{5} \times 5 \times \frac{1}{9} } \\ \\ E = \frac{2}{4 \times \frac{1}{9} }$

Como ya cancelamos 8, 7, 6 y 5. Entonces ahora multiplicamos.

$E = \frac{2}{ \frac{4}{9} }$

Invertimos y multiplicamos.

$E = 2 \times \frac{9}{4}$

Usamos esta regla: a x b/c = ab/c

$E = \frac{2 \times 9}{4}$

Multiplicamos.

$E = \frac{18}{4}$

Y finalmente simplificamos.

$\boxed{E = \frac{9}{2} } \: < = \bold{ resultado}$

Por lo que:

La opción correcta es el literal B

Hasta pronto!!