What's diffrence between these cases? / cases formatting centering

Question

I want my pdf cases to look like that

When I try to do it myself, I have this effect:

Here is my latex code:

\begin{equation*}
g(x)=
\begin{cases}
\frac{x}{x-1} & \textrm{dla}\quad x<-1, \\
2\sin{\pi x} & \textrm{dla}\quad x \in \langle -1,3), \\
\frac{3x+1}{8x} & \textrm{dla}\quad x \in \langle 3,6 \rangle , \\
4x^3 & \textrm{dla}\quad x>6.
\end{cases}
\end{equation*}

Please fix my code

Answer 1

Edit: now is considered @Barbara Beeton comment.

Not with cases but array works fine:

\documentclass[margin=3mm, varwidth]{standalone}
\usepackage{amsmath}
\begin{document}
[
g(x)=
\left{\begin{array}{clc}
\frac{x}{x-1}   & \textrm{dla}  & x<-1, \
2\sin{\pi x}    & \textrm{dla}  & x \in \langle -1,3), \
\frac{3x+1}{8x} & \textrm{dla}  & x \in \langle 3,6 \rangle , \
4x^3            & \textrm{dla}  & x>6.
\end{array}\right.
]
\end{document}

If you like to have bigger vertical space between lined, add afte \] command \renewcommand\arraystretch{1.2}. Then r5esult is:

Answer 2

I found this answer helpful. You just add \hfill on the left and right side side of the content you want to be centered. Here is a MWE:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
g(x)=
\begin{cases}
\hfill \frac{x}{x-1}\hfill & \textrm{dla}\quad \hfill x<-1,\hfill \
\hfill 2\sin{\pi x}\hfill & \textrm{dla}\quad \hfill  x \in \langle -1,3),\hfill \
\hfill \frac{3x+1}{8x}\hfill & \textrm{dla}\quad \hfill x \in \langle 3,6 \rangle ,\hfill \
\hfill 4x^3\hfill & \textrm{dla}\quad \hfill  x>6.\hfill
\end{cases}
\end{equation}
\end{document}

Here is the output: