Q:

How to create the following symbol?  Fractional function

How to create the following symbol? 

A:

The easiest way is to just use two rules and connect them  with a slash kerned by a little negative space.   This does not scale with the content where a more sophisticated approach is needed, i.e. putting things in a box and measure the height. 
\documentclass{article}
\usepackage{amsmath}
\newcommand\fractional[2]{%
  \underline{#1}\mkern-2mu\raise .1ex \hbox{$\big/$}\mkern-1.5mu\overline{#2}
}
\begin{document}
\[ \varPhi^{n,n}(x) = f_0 + \fractional{x-x_0}{\rho(x_0,x_1)} \]
\end{document}

Here is a variant that scales almost nicely. 
\documentclass{article}
\usepackage{amsmath}
\newcommand\fractional[2]{%
  \mathpalette\dofractional{{#1}{#2}}
}
\newcommand\dofractional[2]{%
  \dofractionalindeed#1#2
}
\newcommand\dofractionalindeed[3]{%
  \setbox0=\hbox{$#1#2$}%
  \setbox1=\hbox{$#1#3$}%
  \ifdim\ht0>\ht1
    \dimen0=\dimexpr\ht0+1pt
  \else
    \dimen0=\dimexpr\ht1+1pt
  \fi
  \ifdim\dp0>\dp1
    \dimen1=\dimexpr\dp0+1pt
  \else
    \dimen1=\dimexpr\dp1+1pt
  \fi
  \rlap{\vrule height -\dimen1 width \wd0 depth \dimexpr\dimen1+\fontdimen8\textfont3}
  \box0
  \mkern-2mu
  \mathord{\left/\vrule height \dimen0 depth \dimen1 width 0pt\right.\kern-\nulldelimiterspace}
  \mkern-2mu
  \rlap{\vrule height \dimexpr\dimen0+\fontdimen8\textfont3 width \wd1 depth -\dimen0}
  \box1
}
\begin{document}
\[ \varPhi^{n,n}(x) = f_0 + \scriptscriptstyle \fractional{x-x_0}{\rho(x_0,x_1)} \]
\[ \varPhi^{n,n}(x) = f_0 + \scriptstyle \fractional{x-x_0}{\rho(x_0,x_1)} \]
\[ \varPhi^{n,n}(x) = f_0 + \fractional{x-x_0}{\rho(x_0,x_1)} \]
\[ \varPhi^{n,n}(x) = f_0 + \textstyle \fractional{\int x-x_0}{\sum \rho(x_0,x_1)} \]
\[ \varPhi^{n,n}(x) = f_0 + \fractional{\int x-x_0}{\sum \rho(x_0,x_1)} \]
\end{document}

A:

The following solution draws the complete line with all three parts in one drawing operation.  The advantages are

proper line join,
constant line width. 

The drawing is done with TikZ (which would also allow to change the line styles, line joins, and line caps). 

The correct line width is extracted from the font dimen register:
\fontdimen8\<text|script|scriptscript>font3

The formula is separated from the line by a gap of three line widths
in \underline and \overline.  Also, TeXs sets an outer margin below/above the line with the amount of one line width. 
\overline uses a cramped math style for the formula.  For example, superscripts are lowered a bit.  LuaTeX has commands for setting the cramped math styles.  Without LuaTeX, the solution uses macro \cramped of package mathtools. 

Implementation with example and test cases:
\documentclass{article}

\usepackage{ifluatex}
\ifluatex
  \IfFileExists{luatex85.sty}{\usepackage{luatex85}}{}
  % LuaTeX provides \<mathstyle>cramped
\fi
\begingroup\expandafter\expandafter\expandafter\endgroup
\expandafter\ifx\csname crampedscriptstyle\endcsname\relax
  \usepackage{mathtools} % for \cramped
  \newcommand*{\SetCrampedStyle}[2]{%
    \cramped[#1]{#2}%
  }
\else
  \newcommand*{\SetCrampedStyle}[2]{%
    {%
      \ifx#1\displaystyle\crampeddisplaystyle
      \else\ifx#1\textstyle\crampedtextstyle
      \else\ifx#1\scriptstyle\crampedscriptstyle
      \else\crampedscriptscriptstyle
      \fi\fi\fi
      #2%
    }%
  }
\fi
\usepackage{tikz}

\makeatletter
\newcommand*{\fractional}[2]{%
  \mathpalette{\@fractional{#1}{#2}}{}%
}
\newcommand*{\fractionalAngle}{65}
\newcommand*{\@fractional}[4]{%
  % #1, #2: arguments of \fractional
  % #3: math style
  % #4: unused
  %
  % Get the line width for this math style
  \edef\@LineWidth{%
    \the\fontdimen8
    \ifx#3\displaystyle\textfont
    \else\ifx#3\textstyle\textfont
    \else\ifx#3\scriptstyle\scriptfont
    \else\scriptscriptfont
    \fi\fi\fi
    3%
  }
  %
  % Set the left and right part in boxes for measurment and usage. 
  % Note the cramped style for the right part as in \overline and \sqrt. 
  \sbox0{$#3#1\m@th$}%
  \sbox2{$#3\SetCrampedStyle{#3}{#2}\m@th$}%
  %
  % Calculate the total height for the slanted line
  \edef\@SlashTotalHeight{%
    \the\dimexpr
      \dp0 + \ht2
      + \@LineWidth * 7 % 2 * (3 [space] + 1/2 [line])
    \relax
  }%
  %
  % Calculate the width of the slanted line
  \pgfmathsetlengthmacro\@SlashWidth{%
    \@SlashTotalHeight * cos(\fractionalAngle)%
  }%
  %
  \begin{tikzpicture}[
    inner sep=0pt,
    outer sep=0pt,
    baseline=(Left.base),
    line width=\@LineWidth,
  ]
    \draw[overlay] % Bounding box is set later
      % Left and right part are set as nodes
      node[anchor=base east] (Left) {\copy0}
      ++(\@SlashWidth, 0)
      node[anchor=base west] (Right) {\copy2}
      %
      % Line is drawn
      (Left.south west)
      ++(0, -3.5\pgflinewidth)
      -- ++(\wd0, 0)
      -- ++(\@SlashWidth, \@SlashTotalHeight)
      -- ++(\wd2, 0)
    ;%
    % Bounding box
    \useasboundingbox[outer sep=-.5\pgflinewidth]
      (Left.south west) ++(0, -5\pgflinewidth)
      (Right.north east) ++(0, 5\pgflinewidth)
    ;%
  \end{tikzpicture}%
}
\makeatother

% Testing
\usepackage{amsmath}
\usepackage{color}
\newcommand*{\Annot}[1]{\text{\scriptsize\quad(#1)}}

\begin{document}
\[ \varPhi^{n,n}(x) = f_0 + \fractional{x-x_0}{\rho(x_0,x_1)} \]
\[
  \underline{x_0}
  \begingroup\color{red}
    \fractional{\color{black}x_0}{\color{black}x^{\color{red}0}}
  \endgroup
  \overline{x^{\color{red}0}}
  \Annot{Positions}
\]
\[
  \def\test{
    {\color{blue}\fractional{\color{black}x_0}{\color{black}x^0}}
  }
  \test\,
  \scriptstyle\test\,
  \scriptscriptstyle\test
  \Annot{Line widths}
\]
\[
  \setlength{\fboxsep}{0pt}
  \setlength{\fboxrule}{.2pt}
  \def\test#1{\textcolor{red}{\fbox{\color{black}$#1$}}}%
  \test{\underline{x_0}}\,
  \test{\fractional{x_0}{x^0}}\,
  \test{\overline{x^0}}
  \Annot{Bounding boxes}
\]
\end{document}

