Question

If x³ – y³ = (x – y) (x² + y² – xy) and x³ + y³ = (x +y)(x² + y² + xy), then (2³ + 3³) divided by (3³ – 2³)

Answer 1

$$\begin{gathered} \frac{2^3+3^3}{3^3-2^3} \\ =\frac{\left(2+3\right)\left[{\left(2\right)}^2+{\left(3\right)}^2-2\times 3\right]}{\left(3-2\right)\left[{\left(3\right)}^2+{\left(2\right)}^2+3\times 2\right]} \\ =\frac{5\left(4+9-6\right)}{1\left(9+4+6\right)} \\ =\frac{5\times 7}{1\times 19} \\ =\frac{35}{19} \end{gathered}$$