Giải thích các bước giải:
$\begin{array}{l} \frac{{{a^2}(b - c) + {b^2}(c - a) + {c^2}(a - b)}}{{{a^4}({b^2} - {c^2}) + {b^4}({c^2} - {a^2}) + {c^4}({a^2} - {b^2})}}\\ = \frac{{{a^2}(b - c) + {b^2}c - {b^2}a + {c^2}a - {c^2}b}}{{{a^4}({b^2} - {c^2}) + {b^4}{c^2} - {b^4}{a^2} + {c^4}{a^2} - {c^4}{b^2}}}\\ = \frac{{{a^2}(b - c) + bc(b - c) - a({b^2} - {c^2})}}{{{a^4}({b^2} - {c^2}) + {b^2}{c^2}({b^2} - {c^2}) - {a^2}({b^4} - {c^4})}}\\ = \frac{{(b - c)({a^2} + bc - a(b + c))}}{{({b^2} - {c^2})({a^4} + {b^2}{c^2} - {a^2}({b^2} + {c^2}))}}\\ = \frac{{(b - c)({a^2} - ab + bc - ac)}}{{({b^2} - {c^2})({a^4} + {b^2}{c^2} - {a^2}{b^2} - {a^2}{c^2})}}\\ = \frac{{a(a - b) - c(a - b)}}{{(b + c)\left[ {{a^2}({a^2} - {b^2}) - {c^2}({a^2} - {b^2})} \right]}}\\ = \frac{{(a - b)(a - c)}}{{(b + c)({a^2} - {b^2})({a^2} - {c^2})}}\\ = \frac{1}{{(a + b)(b + c)(c + a)}} \end{array}$
