分母が違う分数式の加法と減法は通分してから

\def\BunsiA{2}
\def\BunboA{x+1}
\def\BunsiB{1}
\def\BunboB{x-3}
\def\Tenkai{2x-6+x+1}
\def\Kotae{3x-5}

\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*}
&\dfrac{\BunsiA}{\colBX{mistyrose}{$\BunboA$}} + \dfrac{\BunsiB}{\colBX{palegreen}{$\BunboB$}}\\
& 　\colMM{green}{相手の分母からもらう \nwarrow}　\colMM{orange}{\nearrow 相手の分母からもらう}\\
&= \dfrac{\BunsiA \colBX{palegreen}{$(\BunboB$)}}{\colBX{mistyrose}{$(\BunboA)$}\colBX{palegreen}{$(\BunboB)$}} + \dfrac{\BunsiB\colBX{mistyrose}{$(\BunboA)$}}{\colBX{palegreen}{$(\BunboB)$}\colBX{mistyrose}{$(\BunboA)$}}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{\BunsiA(\BunboB)+\BunsiB(\BunboA)}{(\BunboA)(\BunboB)}\\
\\
&= \dfrac{\Tenkai}{(\BunboA)(\BunboB)}\\
\\
&= \dfrac{\Kotae}{(\BunboA)(\BunboB)}\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\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*}
& \dfrac{2}{x^2-1} - \dfrac{1}{x^2+x}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{2}{(x+1)\colBX{mistyrose}{$(x-1)$}} - \dfrac{1}{\colBX{palegreen}{$x$}(x+1)}\\
& 　\colMM{green}{　相手の分母からもらう \nwarrow}　\colMM{orange}{\nearrow 相手の分母からもらう}\\
&= \dfrac{2\colBX{palegreen}{$x$}}{(x+1)\colBX{mistyrose}{$(x-1)$}\colBX{palegreen}{$x$}} - \dfrac{1\colBX{mistyrose}{$(x-1)$}}{\colBX{palegreen}{$x$}(x+1)\colBX{mistyrose}{$(x-1)$}}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{2x-(x-1)}{x(x+1)(x-1)}\\
\\
&= \dfrac{\colBX{violet}{$x+1$}}{x\colBX{violet}{$(x+1)$}(x-1)}\\
\\
&= \dfrac{1}{x(x-1)}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\def\BunsiA{2}
\def\BunboA{x+1}
\def\BunsiB{3}
\def\BunboB{x-2}
\def\Tenkai{2x-4+3x+3}
\def\Kotae{5x-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*}
&\dfrac{\BunsiA}{\colBX{mistyrose}{$\BunboA$}} + \dfrac{\BunsiB}{\colBX{palegreen}{$\BunboB$}}\\
& 　\colMM{green}{相手の分母からもらう \swarrow}　\colMM{orange}{\searrow 相手の分母からもらう}\\
&= \dfrac{\BunsiA \colBX{palegreen}{$(\BunboB$)}}{\colBX{mistyrose}{$(\BunboA)$}\colBX{palegreen}{$(\BunboB)$}} + \dfrac{\BunsiB\colBX{mistyrose}{$(\BunboA)$}}{\colBX{palegreen}{$(\BunboB)$}\colBX{mistyrose}{$(\BunboA)$}}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{\BunsiA(\BunboB)+\BunsiB(\BunboA)}{(\BunboA)(\BunboB)}\\
\\
&= \dfrac{\Tenkai}{(\BunboA)(\BunboB)}\\
\\
&= \dfrac{\Kotae}{(\BunboA)(\BunboB)}\\
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\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*}
& \dfrac{x}{x-1} - \dfrac{1}{x^2-x}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{x}{x-1} - \dfrac{1}{\colBX{palegreen}{$x$}(x-1)}\\
& \colMM{green}{　　　　　　\swarrow 相手の分母からもらう}\\%　\colMM{orange}{\nearrow 相手の分母からもらう}\\
&= \dfrac{x \times\colBX{palegreen}{$x$}}{(x-1)\colBX{palegreen}{$x$}} - \dfrac{1}{\colBX{palegreen}{$x$}(x-1)}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{x^2-1}{x(x-1)}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{(x+1)\colBX{violet}{$(x-1)$}}{x\colBX{violet}{$(x-1)$}}\\
& 　　\colMM{red}{\Darr 約分}\\
&= \dfrac{x+1}{x}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\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*}
& \dfrac{x}{x+1} + \dfrac{3x-1}{x^2-2x-3}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{x}{x+1} + \dfrac{3x-1}{(x+1)\colBX{palegreen}{$(x-3)$}}\\
& \colMM{green}{　　　　　　　　　　\swarrow 相手の分母からもらう}\\%　\colMM{orange}{\nearrow 相手の分母からもらう}\\
&= \dfrac{x \times\colBX{palegreen}{$(x-3)$}}{(x+1)\colBX{palegreen}{$(x-3)$}} + \dfrac{3x-1}{(x+1)\colBX{palegreen}{$(x-3)$}}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{x(x-3)+(3x-1)}{(x+1)(x-3)}\\
\\
&= \dfrac{x^2-3x+3x-1}{(x+1)(x-3)}\\
\\
&= \dfrac{x^2-1}{(x+1)(x-3)}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{\colBX{violet}{$(x+1)$}(x-1)}{\colBX{violet}{$(x+1)$}(x-3)}\\
& 　　\colMM{red}{\Darr 約分}\\
&= \dfrac{x-1}{x-3}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan

\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*}
& \dfrac{3x+5}{x^2-1} - \dfrac{1}{x^2+x}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{3x+5}{(x+1)\colBX{mistyrose}{$(x-1)$}} - \dfrac{1}{\colBX{palegreen}{$x$}(x+1)}\\
& \colMM{orange}{　　相手の分母からもらう\searrow}　\colMM{green}{\swarrow 相手の分母からもらう}\\%　\colMM{orange}{\nearrow 相手の分母からもらう}\\
&= \dfrac{(3x+5) \times \colBX{palegreen}{$x$}}{(x+1)\colBX{mistyrose}{$(x-1)$}\colBX{palegreen}{$x$}} - \dfrac{1\colBX{mistyrose}{$(x-1)$}}{\colBX{palegreen}{$x$}(x+1)\colBX{mistyrose}{$(x-1)$}}\\
& 　　　　\colMM{red}{分母が同じ➡分子だけ計算する}\\
&= \dfrac{x(3x+5)-(x-1)}{x(x+1)(x-1)}\\
\\
&= \dfrac{3x^2+5x-x+1}{x(x+1)(x-1)}\\
\\
&= \dfrac{3x^2+4x+1}{x(x+1)(x-1)}\\
& 　\colMM{red}{分数式➡因数分解！}\\
&= \dfrac{(3x+1)\colBX{violet}{$(x+1)$}}{x\colBX{violet}{$(x+1)$}(x-1)}\\
& 　　\colMM{red}{\Darr 約分}\\
&= \dfrac{3x+1}{x(x-1)}
\end{align*}
%1 orange,bisque
%2 green,palegreen
%3 magenta, violet
%4 deepskyblue, lightcyan