How to prove the serial extension of the natural logarithm?

There is a series for the natural logarithm:
$$ ln (x) = 2 sum _ {n = 1} ^ infty frac { left ( frac {x-1} {3 x + 1} right) ^ {2 n-1} + left ( frac {x-1} {x + 3} right) ^ {2 n-1}} {2 n-1}. $$
I was wondering how to prove it. Any ideas, please let me know!