If x = 999, y = 1000, z = 1001 then the value of $$\frac{{{x^3} + {y^3} + {z^3} - 3xyz}}{{x - y + z}}$$     is?

If x = 999, y = 1000, z = 1001 then the value of $$\frac{{{x^3} + {y^3} + {z^3} - 3xyz}}{{x - y + z}}$$     is? Correct Answer 9

$$\eqalign{ & \therefore {a^3} + {b^3} + {c^3} - 3abc \cr & = \frac{1}{2}\left( {a + b + c} \right)\left \cr & \therefore \frac{{{x^3} + {y^3} + {z^3} - 3xyz}}{{x - y + z}} \cr} $$
$$ = \frac{{\frac{1}{2}\left( {x + y + z} \right)\left}}{{x - y + z}}$$
$$\eqalign{ & = \frac{{\frac{1}{2}\left( {999 + 1000 + 1001} \right)\left( {1 + 1 + 4} \right)}}{{999 - 1000 + 1001}} \cr & = \frac{{\frac{1}{2} \times 6 \times 3000}}{{1000}} \cr & = 9 \cr} $$