If x : y = 3 : 1, then x³ - y³ : x³ + y³ = ?

Solution(By Examveda Team)

$$\eqalign{ & = \frac{x}{y} = \frac{3}{1} \cr & \Rightarrow \frac{{{x^3}}}{{{y^3}}} = \frac{{27}}{1} \cr & \Rightarrow \frac{{{x^3} - {y^3}}}{{{x^3} + {y^3}}} = \frac{{\left( {\frac{{{x^3}}}{{{y^3}}}} \right) - 1}}{{\left( {\frac{{{x^3}}}{{{y^3}}}} \right) + 1}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{27 - 1}}{{27 + 1}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{26}}{{28}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{13}}{{14}} \cr & = \left( {{x^3} - {y^3}} \right):\left( {{x^3} + {y^3}} \right) \cr & = 13:14 \cr} $$