Question

Объясните принцип действий

Answer 1

Расписал каждый шаг, чтобы были понятнее преобразования:

$\cfrac{45\cfrac{10}{63}-44\cfrac{25}{84}}{\biggl( \hspace{-0.6mm} 2\cfrac{1}{3}-1\cfrac{1}{9}\biggr):4-\cfrac{3}{4}\ }:31=\cfrac{\biggl( \hspace{-0.8mm}45+\cfrac{10}{63}\biggr)-\biggl( \hspace{-0.8mm}44+\cfrac{25}{84}\biggr)}{\biggl( \hspace{-0.8mm}\biggl( \hspace{-0.6mm} 2+\cfrac{1}{3}\biggr)-\biggl( \hspace{-0.8mm}1+\cfrac{1}{9}\biggr) \hspace{-0.8mm} \biggr):4-\cfrac{3}{4}\ }:31=$

$=\cfrac{45-44+\cfrac{10}{63}-\cfrac{25}{84}}{\biggl( \hspace{-0.8mm} 2-1+\cfrac{1}{3}-\cfrac{1}{9}\biggr):4-\cfrac{3}{4}\ }:31=\cfrac{1+\cfrac{10*4}{63*4}-\cfrac{25*3}{84*3}}{\biggl( \hspace{-0.8mm} 1+\cfrac{1*3}{3*3}-\cfrac{1}{9}\biggr):4-\cfrac{3}{4}\ }:31=$

$=\cfrac{\cfrac{252}{252}+\cfrac{40}{252}-\cfrac{75}{252}}{\biggl( \hspace{-0.4mm} \cfrac{9}{9}+\cfrac{3}{9}-\cfrac{1}{9}\biggr):\cfrac{4}{1}-\cfrac{3}{4}\ }:31=\cfrac{\cfrac{217}{252}}{\cfrac{11}{9}*\cfrac{1}{4}-\cfrac{3*9}{4*9}\ }:31=\cfrac{\cfrac{217}{252}}{\cfrac{11}{36}-\cfrac{27}{36}\ }:31=$

$=\cfrac{\cfrac{217}{252}}{\ -\cfrac{16}{36}\ \ \ }:31=-\biggl( \cfrac{217}{252} \ : \, \cfrac{16}{36}\hspace{0.3mm}\biggr):31=-\biggl( \cfrac{217}{252} \ * \, \cfrac{36}{16}\hspace{0.3mm}\biggr):31=$

$=-\biggl( \cfrac{31}{36} \ * \, \cfrac{9}{4}\hspace{0.3mm}\biggr):\cfrac{31}{1}=-\biggl( \cfrac{31}{36} \ * \, \cfrac{9}{4}\hspace{0.3mm}\biggr)*\cfrac{1}{31}=-\cfrac{31*9*1}{36*4*31}=-\cfrac{1}{16}$