Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\frac{{{a^3} + {b^3}}}{{{a^3} + {c^3}}} = \frac{{a + b}}{{a + c}}\\
\Leftrightarrow \frac{{\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}}{{\left( {a + c} \right)\left( {{a^2} - ac + {c^2}} \right)}} = \frac{{a + b}}{{a + c}}\\
\Leftrightarrow \frac{{a + b}}{{a + c}}\left( {\frac{{{a^2} - ab + {b^2}}}{{{a^2} - ac + {c^2}}} - 1} \right) = 0\\
\Leftrightarrow \frac{{{a^2} - ab + {b^2}}}{{{a^2} - ac + {c^2}}} = 1\\
\Leftrightarrow {a^2} - ab + {b^2} = {a^2} - ac + {c^2}\\
\Leftrightarrow - a\left( {b - c} \right) + \left( {b - c} \right)\left( {b + c} \right) = 0\\
\Leftrightarrow \left( {b - c} \right)\left( { - a + b + c} \right) = 0\\
\Leftrightarrow - a + b + c = 0\,\,\,\,\,\left( {b \ne c} \right)\\
\Leftrightarrow c = a - b
\end{array}\)
