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

Solution(By Examveda Team)

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