分数式の乗法と除法も約分してから

分数式の乗法と除法

次の式を計算しよう

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x^2-x}
\def\BunboA{x+1}
\def\BunsiB{2}
\def\BunboB{x-1}

\def\BunsiC{x\colBX{mistyrose}{$(x-1)$}}
\def\BunboC{x+1}
\def\BunsiD{2}
\def\BunboD{\colBX{mistyrose}{$x-1$}}

\def\BunsiK{2x}
\def\BunboK{x+1}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \times \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \times \dfrac{\BunsiD}{\BunboD}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiK}{\BunboK}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x^2+x}
\def\BunboA{x+2}
\def\BunsiB{x+1}
\def\BunboB{x^2-4}

\def\BunsiC{x(x+1)}
\def\BunboC{x+2}
\def\BunsiD{x+1}
\def\BunboD{(x+2)(x-2)}

\def\BunsiE{x \colBX{mistyrose}{$(x+1)$}}
\def\BunboE{\colBX{palegreen}{$x+2$}}
\def\BunsiF{\colBX{palegreen}{$(x+2)$}(x-2)}
\def\BunboF{\colBX{mistyrose}{$x+1$}}

\def\BunsiG{x(x-2)}
\def\BunboG{1}


\def\BunsiK{\BunsiG}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \div \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \div \dfrac{\BunsiD}{\BunboD}\\
&       \colMM{red}{\Darr 逆数にして掛ける}\\
&= \dfrac{\BunsiE}{\BunboE} \times \dfrac{\BunsiF}{\BunboF}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiG}{\BunboG}\\
\\
&= \BunsiK
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x^2-4}
\def\BunboA{x^2-3x}
\def\BunsiB{x}
\def\BunboB{x+2}

\def\BunsiC{\colBX{mistyrose}{$(x+2)$}(x-2)}
\def\BunboC{\colBX{palegreen}{$x$}(x-3)}
\def\BunsiD{\colBX{palegreen}{$x$}}
\def\BunboD{\colBX{mistyrose}{$x+2$}}

\def\BunsiK{x-2}
\def\BunboK{x-3}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \times \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \times \dfrac{\BunsiD}{\BunboD}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiK}{\BunboK}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{2x}
\def\BunboA{2x+1}
\def\BunsiB{2x^2-3x-2}
\def\BunboB{x-2}

\def\BunsiC{2x}
\def\BunboC{\colBX{mistyrose}{$2x+1$}}
\def\BunsiD{\colBX{mistyrose}{$(2x+1)$}\colBX{palegreen}{$(x-2)$}}
\def\BunboD{\colBX{palegreen}{$x-2$}}

\def\BunsiK{2x}
\def\BunboK{1}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \times \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \times \dfrac{\BunsiD}{\BunboD}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiK}{\BunboK} = \BunsiK
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x-2}
\def\BunboA{x^2+3x}
\def\BunsiB{x^2-3x}
\def\BunboB{x^2-9}

\def\BunsiC{x-2}
\def\BunboC{x(x+3)}
\def\BunsiD{x(x-3)}
\def\BunboD{(x+3)(x-3)}

\def\BunsiE{x-2}
\def\BunboE{x \colBX{mistyrose}{$(x+3)$}}
\def\BunsiF{\colBX{mistyrose}{$(x+3)$}\colBX{palegreen}{$(x-3)$}}
\def\BunboF{x\colBX{palegreen}{$(x-3)$}}

\def\BunsiG{x-2}
\def\BunboG{x^2}


\def\BunsiK{\BunsiG}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \div \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \div \dfrac{\BunsiD}{\BunboD}\\
&       \colMM{red}{\Darr 逆数にして掛ける}\\
&= \dfrac{\BunsiE}{\BunboE} \times \dfrac{\BunsiF}{\BunboF}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiG}{\BunboG}%\\
%\\
%&= \BunsiK
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x^2-x}
\def\BunboA{x-3}
\def\BunsiB{x^2+5x}
\def\BunboB{x^2+2x-15}

\def\BunsiC{x(x-1)}
\def\BunboC{x-3}
\def\BunsiD{x(x+5)}
\def\BunboD{(x-3)(x+5)}

\def\BunsiE{\colBX{mistyrose}{$x$}(x-1)}
\def\BunboE{\colBX{palegreen}{$x-3$}}
\def\BunsiF{\colBX{palegreen}{$(x-3)$}\colBX{violet}{$(x+5)$}}
\def\BunboF{\colBX{mistyrose}{$x$}\colBX{violet}{$(x+5)$}}

\def\BunsiG{x-1}
\def\BunboG{1}


\def\BunsiK{\BunsiG}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \div \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \div \dfrac{\BunsiD}{\BunboD}\\
&       \colMM{red}{\Darr 逆数にして掛ける}\\
&= \dfrac{\BunsiE}{\BunboE} \times \dfrac{\BunsiF}{\BunboF}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiG}{\BunboG}\\
\\
&= \BunsiK
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

この問題へのリンクはこちら(右クリックで保存)

【解答】

\def\BunsiA{x^2-2x}
\def\BunboA{x-3}
\def\BunsiB{x^2+5x}
\def\BunboB{x^2+2x-15}

\def\BunsiC{x(x-2)}
\def\BunboC{x-3}
\def\BunsiD{x(x+5)}
\def\BunboD{(x-3)(x+5)}

\def\BunsiE{\colBX{mistyrose}{$x$}(x-2)}
\def\BunboE{\colBX{palegreen}{$x-3$}}
\def\BunsiF{\colBX{palegreen}{$(x-3)$}\colBX{violet}{$(x+5)$}}
\def\BunboF{\colBX{mistyrose}{$x$}\colBX{violet}{$(x+5)$}}

\def\BunsiG{x-2}
\def\BunboG{1}


\def\BunsiK{\BunsiG}

\newcommand\colNS[2]{\color{#1}#2\color{black}}
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\color{#1}\scriptsize\bf\bm #2\color{black}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\newcommand\colFR[2]{\textcolor{#1}{\fbox{\color{black}#2}}}
\begin{align*}
& \colMM{red}{\Rightarrow かけ算に分解(因数分解)}\\
\dfrac{\BunsiA}{\BunboA} \div \dfrac{\BunsiB}{\BunboB}
&= \dfrac{\BunsiC}{\BunboC} \div \dfrac{\BunsiD}{\BunboD}\\
&       \colMM{red}{\Darr 逆数にして掛ける}\\
&= \dfrac{\BunsiE}{\BunboE} \times \dfrac{\BunsiF}{\BunboF}\\
&   \colMM{red}{\Darr 約分}\\
&= \dfrac{\BunsiG}{\BunboG}\\
\\
&= \BunsiK
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

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