$${\text{The}}\,{\text{value}}\,{\text{of}}\,\frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + 0.096 + {{\left( {0.1} \right)}^2}}}\,{\text{is}}:$$

Explanation:-

$$\eqalign{ & {\text{Given}}\,{\text{expression}} \cr & = \frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + \left( {0.96 \times 0.1} \right) + {{\left( {0.1} \right)}^2}}} \cr & = \left( {\frac{{{a^3} - {b^3}}}{{{a^2} + ab + {b^2}}}} \right) \cr & = \left( {a - b} \right) \cr & = \left( {0.96 - 0.1} \right) \cr & = 0.86 \cr}$$