\cancel or \bcancel draws non-parallel lines in math mode; looking for better solutions

Question

I have very similar lines in math mode under a \align environment. When I use \cancel or \bcancel it doesn't draw parallel lines for what should be similar width terms.

I think a simple repro would be:

\begin{align}
    f &= \left(\cancel{\frac{\partial v}{\partial x}}\right) \\
    g &= \left(\cancel{\frac{\partial v}{\partial z}}\right)
\end{align}

I tried to cook up some tikz based solutions off of this issue, but the dont work well with say \left(\frac{\partial u}{\partial y} + \cancel{\frac{\partial v}{\partial z}}\right) and produce something like

edit:

Answer 1

The \cancel macro uses internally picture mode, and measures the width and height of its argument to decide the slope of the stroke. The code

\documentclass{article}
\begin{document}
\setbox0=\hbox{$x$}\showthe\wd0
\setbox0=\hbox{$z$}\showthe\wd0
\end{document}

returns

> 5.71527pt.
l.3 \setbox0=\hbox{$x$}\showthe\wd0
> 5.0903pt.
l.4 \setbox0=\hbox{$z$}\showthe\wd0

so the x is minimally wider than the z; minimally, and yet enough to trigger the different slope. The quickest (and lest elegant) solution is to add some manual kerning around the symbols.

I implement here this "solution" by the following work-around: the original definition of \cancel in cancel.sty is

\DeclareRobustCommand\cancel[1]{\ifmmode
  \mathpalette{\@cancel{\@can@slash{}}}{#1}\else 
  \@cancel{\@can@slash{}}\hbox{#1}\fi}

I patch this (hoping Donald won't mind) by adding an optional argument which adds some kerning to the argument of \cancel and subtracts it outside of the cancelled expression, such that the total width remains unchanged.

\documentclass{article}

\usepackage{cancel}

\makeatletter
\DeclareRobustCommand\cancel[2][0]{%
  \ifmmode
    \mkern-#1mu
    \mathpalette{\@cancel{\@can@slash{}}}{\mkern#1mu #2 \mkern#1mu}%
    \mkern-#1mu
  \else
    \dimen@=\dimexpr 1em*#1/18\relax
    \kern-\dimen@
    \@cancel{\@can@slash{}}\hbox{\kern\dimen@ #2\kern\dimen@}%
    \kern-\dimen@
  \fi}
\makeatother

\begin{document}

\[
\cancel{\frac{\partial v}{\partial x}}
\quad
\cancel[1]{\frac{\partial v}{\partial z}}
\quad
\cancel[-1]{\frac{\partial v}{\partial x}}
\quad
\cancel{\frac{\partial v}{\partial z}}
\]

\end{document}

Whether you want to add some width to the fraction containing z or subtract it from the fraction containing x, as Barbara Beeton suggested in her comment), is a matter of taste. (I agree with Barbara, but de gustibus...)