\begin{enumerate}
        \item Compléter les pointillés pour qu'il y est bien égalité.
            \hspace{-1cm}
            \begin{center}
                \Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
                $\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
                \hfill
                \Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
                $\dfrac{\Var{a}}{\Var{b}} = \dfrac{\ldots}{\Var{c}}$
                \hfill
                \Block{set a,b,c = random_str("{a},{b},{b*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
                $\dfrac{\cdots}{\Var{c}} = \dfrac{\Var{a}}{\Var{b}}$
                \hfill
                \Block{set a,b,c = random_str("{a},{b},{a*c}", conditions = ["{a} != {b}", "{a} > 1", "{b}>1","{c}>1"]).split(',')}%
                $\dfrac{\Var{a}}{\Var{b}} = \dfrac{\Var{c}}{\cdots}$
            \end{center}

            \vfill
        \item Faire les calculs suivants en détaillant les étapes (penser à simplifier les fractions quand c'est possible).
            \begin{multicols}{2}
                \begin{enumerate}
                    \Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1", "{a} > 0", "{c} > 0"])}
                \item $A = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "A")}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set e = Expression.random("{a} / {b} + {c} / {b}", ["{b} > 1"])}
                \item $B = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "B")}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{c} > 1", "{d} > 1"])}
                \item $C = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "C")}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set e = Expression.random("{a} / {b} + {c} / {d*b}", ["{b} > 1", "{d} > 1"])}
                \item $D = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "D")}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set e = Expression.random("{a} / {b} * {c}", ["{b} > 1", "{a} > 0", "{c} > 1", "{c} != {b}"])}
                \item $E = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "E")}
                        \end{eqnarray*}
                    \end{solution}
                    \Block{set e = Expression.random("{a} / {b} * {c} / {d}", ["{b} > 1", "{a} > 0", "{c} > 0", "{d} > 1"])}
                \item $F = \Var{e}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{e.simplify().explain() | calculus(name = "F")}
                        \end{eqnarray*}
                    \end{solution}
                \end{enumerate}
            \end{multicols}
        \item Évaluer les expressions suivantes
            \begin{multicols}{2}
                \begin{enumerate}

                \Block{set P = Polynom.random(degree = 1)}
                \Block{set x = Expression.random("{a}")}
                \item $\Var{P}$ en $x = \Var{x}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{P(x).explain()| calculus()}
                        \end{eqnarray*}
                    \end{solution}

                \Block{set P = Polynom.random(degree = 2)}
                \Block{set x = Expression.random("{a}")}
                \item $\Var{P}$ en $x = \Var{x}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{P(x).explain()| calculus()}
                        \end{eqnarray*}
                    \end{solution}

                \Block{set P = Expression.random("{a} x * (x - {b})")}
                \Block{set x = Expression.random("{a}")}
                \item $\Var{P}$ en $x = \Var{x}$

                \Block{set P = Expression.random("({a}x + {b})({c} + {d}x)")}
                \Block{set x = Expression.random("{a}")}
                \item $\Var{P}$ en $x = \Var{x}$

                \end{enumerate}
            \end{multicols}
        \item Réduire les expressions suivantes
        \begin{multicols}{2}
            \begin{enumerate}
                    \Block{set A = Expression.random("{a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item A = $\Var{A}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{A.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}

                    \Block{set B = Expression.random("({b} - {a}) + {a}x + {c} + {d}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item B = $\Var{B}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{B.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}


                    \Block{set C = Expression.random("{a}x^2 + {c} + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item C = $\Var{C}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{C.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}

                    \Block{set D = Expression.random("{a}x^2 + {c}x^2 + {d}x + {d} + {a}x", conditions = ["{a} not in [0,1]", "{d} not in [0,1]"])}
                \item D = $\Var{D}$
                    \begin{solution}
                        \begin{eqnarray*}
                            \Var{D.simplify().explain() | calculus()}
                        \end{eqnarray*}
                    \end{solution}
            \end{enumerate}
        \end{multicols}

\end{enumerate}