thực hiện phép tính : A = 81.( $\frac{12-12/7-12/289-12/85}{4-4/7-4/289-4/85}$ : $\frac{5+5/13+5/169+5/99}{6+6/13+6/169+6/91}$ ) . $\frac{158158158}{711711711}$

Đáp án:

$81\cdot \left(\:\dfrac{12-\dfrac{12}{7}-\dfrac{12}{289}-\dfrac{12}{85}}{4-\dfrac{4}{7}-\dfrac{4}{289}-\dfrac{4}{85}}\::\:\dfrac{5+\dfrac{5}{13}+\dfrac{5}{169}+\dfrac{5}{99}}{6+\dfrac{6}{13}+\dfrac{6}{169}+\dfrac{6}{91}}\:\right)\:\cdot \dfrac{158158158}{711711711}$ $=\dfrac{20753172}{320005}$

Giải thích các bước giải:

$81\cdot \left(\:\dfrac{12-\dfrac{12}{7}-\dfrac{12}{289}-\dfrac{12}{85}}{4-\dfrac{4}{7}-\dfrac{4}{289}-\dfrac{4}{85}}\::\:\dfrac{5+\dfrac{5}{13}+\dfrac{5}{169}+\dfrac{5}{99}}{6+\dfrac{6}{13}+\dfrac{6}{169}+\dfrac{6}{91}}\:\right)\:\cdot \dfrac{158158158}{711711711}$

$=\:81\cdot \left(\:\dfrac{\frac{102192}{10115}}{\dfrac{34064}{10115}}\::\:\dfrac{\frac{91430}{16731}}{\dfrac{7764}{1183}}\:\right)\:\cdot \dfrac{2}{9}$

$=\:81\cdot \left(\:3\::\:\dfrac{320005}{384318}\:\right)\:\cdot \dfrac{2}{9}$

$=\:81\cdot \dfrac{1152954}{320005}\:\cdot \dfrac{2}{9}$

$=\dfrac{81}{1}\cdot \dfrac{1152954}{320005}\cdot \dfrac{2}{9}$

$=\dfrac{81\cdot \:1152954\cdot \:2}{1\cdot \:320005\cdot \:9}$

$=\dfrac{9\cdot \:9\cdot \:1152954\cdot \:2}{2880045}$

$=\dfrac{9\cdot \:9\cdot \:1152954\cdot \:2}{9\cdot \:320005}$

$=\dfrac{9\cdot \:1152954\cdot \:2}{320005}$

$=\dfrac{20753172}{320005}$