Using Tikzmark and Arrows

Question

This is a basic question and I apologize if this program is using the latest version of the tikzmark library not available in CTAN. I posted as far as I got and also the image I am trying to replicate. Please assist in finishing the program.

\documentclass{article}
\usepackage{amsmath,mathtools,geometry}
\usepackage{tikz}
\usetikzlibrary{tikzmark}

\newbox\aebox
\newcommand\aecomment[2][0pt]{%%
  \begin{lrbox}\aebox
    \begin{minipage}[t]{2.5in}
      \raggedright
      \textcolor{blue}{#2}%%
    \end{minipage}%%
  \end{lrbox}%%
  \raisebox{#1}[\height][0pt]{\usebox{\aebox}}}

\begin{document}
For $f(x)=\dfrac{1}{x}$, we have

\begin{align*}
        f(x+h)&=\dfrac{1}{x+h} \\
\shortintertext{then}\\
                    f(x+h)-f(x)&=\dfrac{1}{x+h}-\dfrac{1}{x} \\ \\
                           &=\dfrac{1}{x+h} \cdot \textcolor{red} 
   {\dfrac{\tikzmarknode{C}{x}}{x}}-\dfrac{1}{x}\cdot \textcolor{red} 
   {\dfrac{x+h}{x+h}} && \aecomment[1.3ex]{\textcolor{red}{\tikzmarknode{A} 
   {}Multiplying by $1$ to get a common denominator}}\\
   \end{align*}

\begin{tikzpicture}[overlay,remember picture]
\draw[red] ([yshift=3pt,xshift=-5pt]A.west) -- ++(-7pt,0pt)-- ++ (0pt,7pt);
\end{tikzpicture}


\end{document}

I am trying to recreate

I keep compiling errors each attempt to recreate the arrows.....

Answer 1

The newest tikzmarklibrary is now for a while in the standard TeX distributions, so everything is fine, and it is really easy to draw the arrows.

\documentclass{article}
\usepackage{amsmath,mathtools,geometry}
\usepackage{tikz}
\usetikzlibrary{tikzmark}

\newbox\aebox
\newcommand\aecomment[2][0pt]{%%
  \begin{lrbox}\aebox
    \begin{minipage}[t]{2.5in}
      \raggedright
      \textcolor{blue}{#2}%%
    \end{minipage}%%
  \end{lrbox}%%
  \raisebox{#1}[\height][0pt]{\usebox{\aebox}}}

\begin{document}
For $f(x)=\dfrac{1}{x}$, we have

\begin{align*}
        f(x+h)&=\dfrac{1}{x+h} \\
\shortintertext{then}\\
                    f(x+h)-f(x)&=\dfrac{1}{x+h}-\dfrac{1}{x} \\ \\
                           &=\dfrac{1}{x+h} \cdot \textcolor{red} 
   {\dfrac{\tikzmarknode{C}{x}}{x}}-\dfrac{1}{x}\cdot \textcolor{red} 
   {\dfrac{x\tikzmarknode{C'}{+}h}{x+h}} && \aecomment[1.3ex]{\textcolor{red}{\tikzmarknode{A} 
   {}Multiplying by $1$ to get a common denominator}}\\
   \end{align*}

\begin{tikzpicture}[overlay,remember picture]
\draw[red,-latex] ([yshift=3pt,xshift=-5pt]A.west) -- ++(-7pt,0pt)-- ++ (0pt,12pt)
coordinate (aux)-| (C.north);
\draw[red,-latex] (aux) -| (C'.north);
\end{tikzpicture}


\end{document}