Discussion

Explanation:

Given, (a^-1 + b^-1) ÷ (a^-3 + b^-3)

= $\frac{{\displaystyle \frac{1}{\mathrm{a}}}+{\displaystyle \frac{1}{\mathrm{b}}}}{\frac{1}{{\mathrm{a}}^3}+\frac{1}{{\mathrm{b}}^3}}$

= $\frac{{\displaystyle \frac{a+b}{ab}}}{{\displaystyle \frac{a^3+b^3}{{\left(ab\right)}^3}}}$

= $\frac{{\displaystyle (a+b){\left(ab\right)}^2}}{{\displaystyle (a+b)(a^2-ab+b^2)}}$

= $\frac{{\displaystyle {\left(ab\right)}^2}}{{\displaystyle (a^2-ab+b^2)}}$

Hence, option (d).

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