\( %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Mes commandes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \newcommand{\multirows}[3]{\multirow{#1}{#2}{$#3$}}%pour rester en mode math \renewcommand{\arraystretch}{1.3}%pour augmenter la taille des case \newcommand{\point}[1]{\marginnote{\small\vspace*{-1em} #1}}%pour indiquer les points ou le temps \newcommand{\dpl}[1]{\displaystyle{#1}}%megamode \newcommand{\A}{\mathscr{A}} \newcommand{\LN}{\mathscr{N}} \newcommand{\LL}{\mathscr{L}} \newcommand{\K}{\mathbb{K}} \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\M}{\mathcal{M}} \newcommand{\D}{\mathbb{D}} \newcommand{\E}{\mathcal{E}} \renewcommand{\P}{\mathcal{P}} \newcommand{\G}{\mathcal{G}} \newcommand{\Kk}{\mathcal{K}} \newcommand{\Cc}{\mathcal{C}} \newcommand{\Zz}{\mathcal{Z}} \newcommand{\Ss}{\mathcal{S}} \newcommand{\B}{\mathbb{B}} \newcommand{\inde}{\bot\!\!\!\bot} \newcommand{\Proba}{\mathbb{P}} \newcommand{\Esp}[1]{\dpl{\mathbb{E}\left(#1\right)}} \newcommand{\Var}[1]{\dpl{\mathbb{V}\left(#1\right)}} \newcommand{\Cov}[1]{\dpl{Cov\left(#1\right)}} \newcommand{\base}{\mathcal{B}} \newcommand{\Som}{\textbf{Som}} \newcommand{\Chain}{\textbf{Chain}} \newcommand{\Ar}{\textbf{Ar}} \newcommand{\Arc}{\textbf{Arc}} \newcommand{\Min}{\text{Min}} \newcommand{\Max}{\text{Max}} \newcommand{\Ker}{\text{Ker}} \renewcommand{\Im}{\text{Im}} \newcommand{\Sup}{\text{Sup}} \newcommand{\Inf}{\text{Inf}} \renewcommand{\det}{\texttt{det}} \newcommand{\GL}{\text{GL}} \newcommand{\crossmark}{\text{\ding{55}}} \renewcommand{\checkmark}{\text{\ding{51}}} \newcommand{\Card}{\sharp} \newcommand{\Surligne}[2]{\text{\colorbox{#1}{ #2 }}} \newcommand{\SurligneMM}[2]{\text{\colorbox{#1}{ #2 }}} \newcommand{\norm}[1]{\left\lVert#1\right\rVert} \renewcommand{\lim}[1]{\underset{#1}{lim}\,} \newcommand{\nonor}[1]{\left|#1\right|} \newcommand{\Un}{1\!\!1} \newcommand{\sepon}{\setlength{\columnseprule}{0.5pt}} \newcommand{\sepoff}{\setlength{\columnseprule}{0pt}} \newcommand{\flux}{Flux} \newcommand{\Cpp}{\texttt{C++\ }} \newcommand{\Python}{\texttt{Python\ }} %\newcommand{\comb}[2]{\begin{pmatrix} #1\\ #2\end{pmatrix}} \newcommand{\comb}[2]{C_{#1}^{#2}} \newcommand{\arrang}[2]{A_{#1}^{#2}} \newcommand{\supp}[1]{Supp\left(#1\right)} \newcommand{\BB}{\mathcal{B}} \newcommand{\arc}[1]{\overset{\rotatebox{90}{)}}{#1}} \newcommand{\modpi}{\equiv_{2\pi}} \renewcommand{\Re}{Re} \renewcommand{\Im}{Im} \renewcommand{\bar}[1]{\overline{#1}} \newcommand{\mat}{\mathcal{M}} \newcommand{\und}[1]{{\mathbf{\color{red}\underline{#1}}}} \newcommand{\rdots}{\text{\reflectbox{$\ddots$}}} \newcommand{\Compa}{Compa} \newcommand{\dint}{\dpl{\int}} \newcommand{\intEFF}[2]{\left[\!\left[#1 ; 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Exercice

L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.

Exercice


Calculer \[\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\left(-4+\dfrac{20}{3}+0\right)+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{\dfrac{\dfrac{-4}{\dfrac{13}{11}}}{\dfrac{107}{4}}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\left(-4+\dfrac{20}{3}+0\right)+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{\dfrac{\dfrac{-4}{\dfrac{13}{11}}}{\dfrac{107}{4}}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}=\dfrac{2266902}{35917511}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\left(\dfrac{8}{3}+0\right)+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{\dfrac{\dfrac{-4}{\dfrac{13}{11}}}{\dfrac{107}{4}}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{\dfrac{\dfrac{-4}{\dfrac{13}{11}}}{\dfrac{107}{4}}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{\dfrac{-\dfrac{44}{13}}{\dfrac{107}{4}}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{61}{5}+\dfrac{58}{9}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\left(\dfrac{107}{4}+\dfrac{20}{11}\right)-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}-\left(-4-4-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}-\left(-8-12+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}-\left(-20+\dfrac{13}{11}\right)}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{\dfrac{\dfrac{-\dfrac{61}{5}}{-\dfrac{71}{2}}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{\dfrac{\dfrac{122}{355}}{-\dfrac{87}{7}}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{\dfrac{\dfrac{-\dfrac{87}{7}}{\dfrac{20}{3}}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{\dfrac{-\dfrac{261}{140}}{\dfrac{13}{11}}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{-\dfrac{2871}{1820}}{-\dfrac{107}{8}}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{20}{11}-\dfrac{8}{3}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{-\dfrac{28}{33}+\dfrac{25}{2}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{769}{66}+\dfrac{71}{2}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{1556}{33}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{-\dfrac{176}{1391}}{-\dfrac{259}{45}}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{1556}{33}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{\dfrac{\dfrac{7920}{360269}}{-4}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{1556}{33}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{1257}{44}+\dfrac{207}{11}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{1556}{33}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{2085}{44}}}{-\dfrac{854}{30885}-\dfrac{5742}{48685}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{\dfrac{1556}{33}}{\dfrac{107}{4}}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{2085}{44}}}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{\dfrac{\dfrac{6224}{3531}}{-4}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{2085}{44}}}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{-\dfrac{1556}{3531}}{-\dfrac{107}{8}}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{2085}{44}}}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{12448}{377817}-\dfrac{\dfrac{\dfrac{0}{-\dfrac{1980}{360269}}}{\dfrac{2085}{44}}}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{12448}{377817}-\dfrac{\dfrac{0}{\dfrac{2085}{44}}}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{12448}{377817}-\dfrac{0}{-\dfrac{43783732}{300727245}}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{\dfrac{-4}{-4}}}{-4}}{\dfrac{12448}{377817}-0+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{1}}{-4}}{\dfrac{12448}{377817}-0+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{1}}{-4}}{\dfrac{12448}{377817}+12+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{1}}{-4}}{\dfrac{4546252}{377817}+\dfrac{71}{2}}\\&=&\dfrac{\dfrac{\dfrac{-12}{1}}{-4}}{\dfrac{35917511}{755634}}\\&=&\dfrac{\dfrac{-12}{-4}}{\dfrac{35917511}{755634}}\\&=&\dfrac{3}{\dfrac{35917511}{755634}}\\&=&\dfrac{2266902}{35917511}\\ \end{eqnarray*}