Displaying a set of equations lined up by first equals sign

I am trying to display the content of the following, central, but so that the first equals sign in each lines up. This is with ones of the sugested ways to do this that I found, but it did not work.

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\begin{equation*}
\begin{aligned}
$\frac{6}{7}  &{}= R_1 + \frac{1}{2}$,

\newline
$R_1  &{}=  \frac{6}{7} - \frac{1}{2} = \frac{6}{14} = R_2 + \frac{1}{3}$,

\newline
$R_2  &{}=  \frac{6}{14} - \frac{1}{3} = \frac{2}{21} = R_3 + \frac{1}{11}$,

\newline
$R_3  &{}=  \frac{2}{21} - \frac{1}{11} = \frac{1}{231}$,

\newline
$\frac{6}{7} =  \frac{1}{2} + \frac{1}{3} + \frac{1}{11} + \frac{1}{231}$,
\end{aligned}
\end{equation*}
\newline