Question

Solve:
$\frac{3-\sqrt{5}}{3+2\sqrt{5}}=a\sqrt{5}-\frac{19}{11}$

Answer 1

$\frac{3-\sqrt{5}}{3+2\sqrt{5}}=a\sqrt{5}-\frac{19}{11}$

$a\sqrt{5}=\frac{9\sqrt{5}-19}{11}+\frac{19}{11}$

$\frac{a\sqrt{5}}{\sqrt{5}}=\frac{\frac{9\sqrt{5}-19}{11}}{\sqrt{5}}+\frac{\frac{19}{11}}{\sqrt{5}}$

$a=\frac{\frac{9\sqrt{5}-19}{11}+\frac{19}{11}}{\sqrt{5}}$

$a=\frac{\frac{9\sqrt{5}}{11}}{\sqrt{5}}$

$a=\frac{9\sqrt{5}}{11\sqrt{5}}$

$a=\frac{9}{11}$