What is the value of $$\frac{{\left( {{a^2} + {b^2}} \right)\left( {a - b} \right) - \left( {{a^3} - {b^3}} \right)}}{{{a^2}b - a{b^2}}}?$$

$$\eqalign{ & \frac{{\left( {{a^2} + {b^2}} \right)\left( {a - b} \right) - \left( {{a^3} - {b^3}} \right)}}{{{a^2}b - a{b^2}}} \cr & = \frac{{\left( {{a^2} + {b^2}} \right)\left( {a - b} \right) - \left( {{a^3} - {b^3}} \right)}}{{ab\left( {a - b} \right)}} \cr & = \frac{{\left( {a - b} \right)\left( {{a^2} + {b^2} - {a^2} - {b^2} - ab} \right)}}{{ab\left( {a - b} \right)}} \cr & = - 1 \cr} $$