Giải thích các bước giải:
\[\begin{array}{l}
a;\\
\frac{{a{x^4} - {a^4}x}}{{{a^2} + ax + {x^2}}} = \frac{{ax\left( {{x^3} - {a^3}} \right)}}{{{a^2} + ax + {x^2}}} = \frac{{ax\left( {x - a} \right)\left( {{x^2} + xa + {a^2}} \right)}}{{{a^2} + ax + {x^2}}} = ax\left( {x - a} \right)\\
b;\\
\frac{{{x^3} + {x^2} - 6x}}{{{x^3} - 4x}} = \frac{{x\left( {{x^2} + x - 6} \right)}}{{x\left( {{x^2} - 4} \right)}} = \frac{{x\left( {x + 3} \right)\left( {x - 2} \right)}}{{x\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{x + 3}}{{x + 2}}\\
c,\\
\frac{{{x^2} - {y^2}}}{{{x^2} - {y^2} + xz - yz}} = \frac{{\left( {x - y} \right)\left( {x + y} \right)}}{{\left( {x - y} \right)\left( {x + y} \right) + z\left( {x - y} \right)}} = \frac{{\left( {x - y} \right)\left( {x + y} \right)}}{{\left( {x - y} \right)\left( {x + y + z} \right)}} = \frac{{x + y}}{{x + y + z}}\\
d,\\
\frac{{{{\left( {a + b} \right)}^2} - {c^2}}}{{a + b + c}} = \frac{{\left( {a + b + c} \right)\left( {a + b - c} \right)}}{{a + b + c}} = a + b - c
\end{array}\]
