$$\frac { 3 + 2 \sqrt { 5 } } { 3 - 2 \sqrt { 5 } } = p + q \sqrt { 5 } , 11 ( p + q )$$
$p=\frac{\sqrt{5}r+5r+41\sqrt{5}+89}{44}$
$q=\frac{-\left(\sqrt{5}+1\right)r-41\sqrt{5}-89}{44}$
