ABC26GN2918 · Ratio and Proportion

$\frac{x+y}{x-y} = \frac{7}{3} \Rightarrow 3(x+y) = 7(x-y) \Rightarrow 3x+3y = 7x-7y \Rightarrow 4x = 10y \Rightarrow \frac{x}{y} = \frac{5}{2}$. $\frac{x^3+y^3}{x^3-y^3} = \frac{\left(\frac{x}{y}\right)^3+1}{\left(\frac{x}{y}\right)^3-1} = \frac{\left(\frac{5}{2}\right)^3+1}{\left(\frac{5}{2}\right)^3-1} = \frac{\frac{125}{8}+1}{\frac{125}{8}-1} = \frac{\frac{133}{8}}{\frac{117}{8}} = \frac{133}{117}$. Hence, $(x^3+y^3):(x^3-y^3) = 133:117$.