The value of $$\frac{{{{\left( {2.3} \right)}^3} - 0.027}}{{{{\left( {2.3} \right)}^2} + 0.69 + 0.09}}$$    is :

$$\eqalign{ & = \frac{{{{\left( {2.3} \right)}^3} - 0.027}}{{{{\left( {2.3} \right)}^2} + 0.69 + 0.09}} \cr & = \frac{{{{\left( {2.3} \right)}^3} - {{\left( {0.03} \right)}^3}}}{{{{\left( {2.3} \right)}^2} + \left( {2.3 \times 0.3} \right) + {{\left( {0.3} \right)}^2}}} \cr & = \left[ {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right] \cr & = \left( {a - b} \right) \cr & = \left( {2.3 - 0.3} \right) \cr & = 2 \cr} $$