Giải thích các bước giải:
Giả sử: $\frac{a}{b} = \frac{c}{d} = k \Rightarrow \left\{ \begin{array}{l}
a = b.k\\
c = d.k
\end{array} \right.$
khi đó ta có:
$\begin{array}{l}
{\left( {\frac{{a - b}}{{c - d}}} \right)^3} = {\left( {\frac{{b.k - b}}{{d.k - d}}} \right)^3} = {\left( {\frac{{b\left( {k - 1} \right)}}{{d.\left( {k - 1} \right)}}} \right)^3} = \frac{{{b^3}}}{{{d^3}}}\\
\left( {\frac{{{a^3} + {b^3}}}{{{c^3} + {d^3}}}} \right) = \frac{{{{\left( {b.k} \right)}^3} + {b^3}}}{{{{\left( {d.k} \right)}^3} + {d^3}}} = \frac{{{b^3}\left( {{k^3} + 1} \right)}}{{{d^3}\left( {{k^3} + 1} \right)}} = \frac{{{b^3}}}{{{d^3}}}\\
\Rightarrow {\left( {\frac{{a - b}}{{c - d}}} \right)^3} = \frac{{{a^3} + {b^3}}}{{{c^3} + {d^3}}}\left( {dieu\,phai\,chung\,\min h} \right)
\end{array}$
