Question

If $a:b=\frac{2}{3}$, then find the value of $\frac{a+2b}{a-3b}$.

Answer 1

If $a:b=2:3$, then
$\frac{a+2b}{a-3b}=\frac{\frac{2b}{3}+2b}{\frac{2b}{3}-3b}=\frac{\frac{2b+6b}{3}}{\frac{2b-9b}{3}}$
$=\frac{8b}{-7b}=-\frac{8}{7}$