Đáp án:
c) \(\left( {x + 1} \right)\left( {x - 5} \right)\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{{\left( {{x^2} - {y^2}} \right)\left( {{x^2} + {y^2}} \right)}}{{\left( {x + y} \right)\left( {{x^2} - xy + y} \right)}} = \dfrac{{\left( {x - y} \right)\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)}}{{\left( {x + y} \right)\left( {{x^2} - xy + y} \right)}}\\
= \dfrac{{\left( {x - y} \right)\left( {{x^2} + {y^2}} \right)}}{{{x^2} - xy + y}}\\
b)\dfrac{{5.7.\left( {x - y} \right)\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)}}{{7.11{{\left( {x - y} \right)}^2}{{\left( {x + 3} \right)}^3}}}\\
= \dfrac{{5\left( {x + y} \right)\left( {{x^2} + {y^2}} \right)}}{{11\left( {x - y} \right){{\left( {x + 3} \right)}^3}}}\\
c)\dfrac{{\left( {{x^2} + 3x + 2} \right)\left( {x - 5} \right)\left( {x + 5} \right)}}{{{x^2} + 7x + 10}}\\
= \dfrac{{\left( {x + 1} \right)\left( {x + 2} \right)\left( {x - 5} \right)\left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 2} \right)}}\\
= \left( {x + 1} \right)\left( {x - 5} \right)
\end{array}\)
