使用 pgfplots 生成函数的斜率场

Question

我正在尝试绘制函数的斜率场：(x-y)/(x+y)。这是我目前得到的结果：

\documentclass{report}

\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.8}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    view={0}{90},
    xmax=1, xmin=0,
    ymax=0.6, ymin=-0.6,
    domain=0:1,
    axis x line=middle,
    axis y line=middle,
    axis line style={<->},
    xlabel={$x$},
    ylabel={$y$},
    grid style={solid,gray!40},
    ticks=none,
    ]
    \addplot3[
      gray,
      quiver={
        u={1},
        v={(x-y)/(x+y)},
        scale arrows=0.3,
      }] (x,y,0);
      % \addplot[thick,red,domain=-10:10,samples=1000] {(x-y)/(x+y)};
  \end{axis}
\end{tikzpicture}
\end{document}

但它看起来是这样的：

我希望它看起来像这样：

如何绘制包含x和y项的函数\addplot？当您取消注释所提供代码中的行时，它会给出一条错误消息：

! Package pgfplots Error: Sorry, you can't use 'y' in this context. PGFPlots ex
pected to sample a line, not a mesh. Please use the [mesh] option combined with
 [samples y>0] and [domain y!=0:0] to indicate a twodimensional input domain.

See the pgfplots package documentation for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.28 ...domain=-10:10,samples=1000] {(x-y)/(x+y)};
                                                  
?

最后，我怎样才能使斜率场中所有线的长度保持恒定，就像上图所示的那样？