# Reason of variation in sizes of fractions?

I am not an expert but in my humble opinion the problem will be `\left(`

... `\right)`

which does not give a right size, sometimes, to the formula into the rounded brackets. I have used instead `\bigl(`

and `\bigr)`

.

```
\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
\begin{document}
\[\sqrt{1 + \bigl(\tfrac{\partial z}{\partial x} \bigr)^2 + \bigl(\tfrac{\partial z}{\partial y} \bigr)^2}\]
\end{document}
```

Your fractions are different sizes simply because "x" and "y" are not the same size: "y" is taller. Because you use `\left`

and `\right`

, the size of the parentheses adapt to their content, so the second pair gets bigger than the first one. This can be confirmed by `\smash`

ing the "y" and adding a `\vphantom{x}`

to use the height of "x" in both fractions, which I did in the second example here.

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\sqrt{1 + \left( \tfrac{\partial z}{\partial x} \right)^2 + \left(\tfrac{\partial z}{\partial y} \right)^2}
\qquad
\sqrt{1 + \left( \tfrac{\partial z}{\partial x} \right)^2 + \left(\tfrac{\partial z}{\partial \smash{y}\vphantom{x}} \right)^2}
\]
\end{document}
```

As @Sebastiano recommended, the best solution is probably to use `\bigl( ... \bigr)`

(or similar commands) rather than `\left( ... \right)`

.