Question

Find the value of a, if 3-root 5/3+2 root 5= a root 5 - 19/11

Answer 1

In question there are no parentheses, so actions are performed one after the other:
$3-\frac{\sqrt5}3+2\sqrt5=a\sqrt5-\frac{19}{11}\\a\sqrt5=\frac{(6-1)\sqrt5}{3}+\frac{33+19}{11}\\a=\frac53+\frac{52}{11\sqrt5}=\frac53+\frac{52\sqrt5}{55}$