Problem with fraction and align environment - “&” symbol

Question

I am new in LaTeX, thus I need your help.

I want to align the \leq symbol under the + symbol. The problem is that the + symbol is contained inside a fraction, therefore, the \begin{aligned}--\end{aligned} environment, does not allow me to insert the & symbol inside this certain fraction.

How can I achieve this without having any problems?

An example:

$\displaystyle \begin{aligned}
\sqrt{\frac{2x}{y **&+** z}}+\sqrt{\frac{2y}{z+x}}+\sqrt{\frac{2z}{x+y}}\\
&\leq 3.
\end{aligned}$

P.S I have searched the site but I haven't found anything similar with my problem. (maybe I am not searching, right?)

Answer 1

I would recommend a different approach and that is to use an \hphantom to insert the appropriate amount of horizontal space:

Notes:

• I used \hphantom instead of \phantom as I did not want the vertical size of \sqrt{{\frac{2x}{y **}}} to affect the second row.
• Alignment points located inside other terms such as \sqrt and frac are not usually this easy to do, and David's solution was quite clever in moving it outside and inserting a negative \hspace. I personally would never have thought of that as I tend to think of alignment form the left moving towards the right.

Code:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$\displaystyle \begin{aligned}
&\sqrt{\frac{2x}{y **+** z}}+\sqrt{\frac{2y}{z+x}}+\sqrt{\frac{2z}{x+y}}\\
&\hphantom{\sqrt{{\frac{2x}{y **}}}}\leq 3.
\end{aligned}$

\end{document}

Answer 2

If you have some multline equation to typeset and you don't align globally by = or \leq, I would suggest you to try:

\begin{multline}
  f/i/r/s/t + l/i/n/e
\\
  \leq s/e/c/o/n/d + l/i/n/e
.\end{multline}

And surely you should use proper displayed equation and never ever do $\displaystyle. The env multline is provided by the package amsmath and you do not put it inside another environment (it is similar to equation). As well, it has a starred variant multline* that suppresses the numbering.

Answer 3

This is a seriously odd place to align, what mathematical meaning do you mean to convey by aligning the inequality with the + in the subterm?

However:

\documentclass{article}
\usepackage{amsmath}
\newlength\mlength

\begin{document}

\settowidth{\mlength}{$+**z$}
$\displaystyle \begin{aligned}
\sqrt{\frac{2x}{y **+** z}}&+\sqrt{\frac{2y}{z+x}}+\sqrt{\frac{2z}{x+y}}\\
&\hspace{-\mlength}\leq 3.
\end{aligned}$

\end{document}