$$\frac{ 7+3 \sqrt{ 5 } }{ 3+ \sqrt{ 5 } } - \frac{ 7-3 \sqrt{ 5 } }{ 3- \sqrt{ 5 } } =a+b \sqrt{ 5 }$$
$a=\sqrt{5}\left(1-b\right)$
$b=-\frac{\sqrt{5}a}{5}+1$
