Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{{a^2}}}{{ab + {b^2}}} + \dfrac{{{b^2}}}{{ab - {a^2}}} - \dfrac{{{a^2} + {b^2}}}{{ab}}\\
= \dfrac{{{a^2}}}{{b\left( {a + b} \right)}} + \dfrac{{{b^2}}}{{a\left( {b - a} \right)}} - \dfrac{{{a^2} + {b^2}}}{{ab}}\\
= \dfrac{{{a^2}}}{{b\left( {a + b} \right)}} - \dfrac{{{b^2}}}{{a\left( {a - b} \right)}} - \dfrac{{{a^2} + {b^2}}}{{ab}}\\
= \dfrac{{{a^2}.a.\left( {a - b} \right) - {b^2}.b.\left( {a + b} \right) - \left( {{a^2} + {b^2}} \right)\left( {a + b} \right)\left( {a - b} \right)}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{{a^3}\left( {a - b} \right) - {b^3}\left( {a + b} \right) - \left( {{a^2} + {b^2}} \right)\left( {{a^2} - {b^2}} \right)}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{{a^4} - {a^3}b - {b^3}a - {b^4} - \left( {{a^4} - {b^4}} \right)}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{{a^4} - {a^3}b - {b^3}a - {b^4} - {a^4} + {b^4}}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{ - {a^3}b - a{b^3}}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{ - ab\left( {{a^2} + {b^2}} \right)}}{{ab\left( {a - b} \right)\left( {a + b} \right)}}\\
= \dfrac{{ - \left( {{a^2} + {b^2}} \right)}}{{{a^2} - {b^2}}}\\
= \dfrac{{{a^2} + {b^2}}}{{{b^2} - {a^2}}}
\end{array}\)
