If \(\frac{\sqrt{13}-1}{\sqrt{13}+1}=a+b \sqrt{13} \) , then what are the values of a and b?
1
\(a=\frac{5}{6}, b=-\frac{1}{6} \)
2
a = 0, b = 0
3
\(a=\frac{1}{6}, b=-\frac{1}{6} \)
4
\(a=\frac{7}{6}, b=-\frac{\mathbf{1}}{6} \)
5
None of the above