If a : b = 2 : 3, then find the value of (a^3+2ab^2)/(b^3-2a^2b)

a : b = 2 : 3

a = 2, b = 3

Now,

⇒ \(\frac{a^{3}\;+\;2ab^{2}}{b^{3}\;-\;2a^{2}b}\)

= \(\frac{2^{3}\;+\;2\;×\;2\;×\;3^{2}}{3^{3}\;-\;2\;×\;2^{2}\;×\;3}\)

= \(\frac{8\;+\;36}{27\;-\;24}\)

= \(\frac{44}{3}\)

= 14\(\frac{2}{3}\)