Question

If $\frac{a}{b}=\frac{8}{3}$, find $\frac{4a+5b}{4a-5b}$.

Answer 1

$\frac{4a+5b}{4a-5b}=\frac{b(4\left(\frac{a}{b}\right)+5)}{b(4\left(\frac{a}{b}\right)-5)}=\frac{4\left(\frac{8}{3}\right)+5}{4\left(\frac{8}{3}\right)-5}=\frac{32+15}{32-15}=\frac{47}{17}$.