# how to make a balanced fraction

Package `mathtools`

provides the command `\mathrlap`

to write something to the right in math mode without allocating the space.

LaTeX's `\hphantom`

can also be used in math mode to reserve horizontal space without typesetting the argument. For version with the long fraction line, an invisible subscript is put to the left.

```
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[
\frac{x}{\lVert x\rVert\mathrlap{_1}}
=
\frac{x}{\hphantom{_1} \lVert x\rVert_1}
\]
\end{document}
```

The length of the fraction bar can be controlled by adding symmetrical space:

```
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align*}
&\frac{x}{\lVert x\rVert\mathrlap{_1}}
=
\frac{x}{\,\lVert x\rVert\mathrlap{_1}\,}
=
\frac{x}{\>\lVert x\rVert\mathrlap{_1}\>}
=
\frac{x}{\:\lVert x\rVert\mathrlap{_1}\:}
\\
&\frac{x}{\hphantom{_1}\lVert x\rVert_1}
=
\frac{x}{\!\hphantom{_1}\lVert x\rVert_1\!}
=
\frac{x}{\!\!\hphantom{_1}\lVert x\rVert_1\!\!}
\end{align*}
\end{document}
```

In the first case the subscript is decouple with the previous fence, because it is the in `\mathrlap`

. The following example, fixes this by setting the denominator twice. The first time with the subscript, but the complete expression in `\mathclap`

so that the subscript is right after the fence. The second time the denominator is set without the subscript in `\hphantom`

for the space.

```
\documentclass{article}
\usepackage{mathtools}
\usepackage{mleftright}
\begin{document}
\[
\frac{a}{ \mleft\lVert\frac{b}{c}\mright\rVert\mathrlap{_1}}
=
\frac{a}{ \mathrlap{\mleft\lVert\frac{b}{c}\mright\rVert_1}
\hphantom{\mleft\lVert\frac{b}{c}\mright\rVert}}
=
\frac{a}{\hphantom{_1}\mleft\lVert\frac{b}{c}\mright\rVert_1}
\]
\end{document}
```

**Remarks:**

Package

`mleftright`

is used for`\mleft`

and`\mright`

that use`\left`

and`\right`

but without the additional horizontal spacing.`\lVert`

and`\rVert`

denotes that the`\lVert`

is used as left fence and`\rVert`

serves as right delimiter.

Simplest was is to move the subscript outside of the `\frac{}{}`

:

```
\frac{x}{\left\Vert x \right\Vert}_{\!1}
```

and a little negative thinspace for better spacing. The second option can be achieved with a careful use of `\makebox`

and `\hphantom`

:

## Code:

```
\documentclass{article}
\usepackage{mathtools}
\newcommand*{\WideAs}[2]{\makebox[\widthof{$#1$}][c]{$#2$}}
\begin{document}
\begin{equation*}
\frac{x}{\left\Vert x \right\Vert}_{\!1}
\quad
\frac{\WideAs{\left\Vert x \right\Vert}{x}\hphantom{{}_1}}{\left\Vert x \right\Vert_1}
\end{equation*}
\end{document}
```