Đáp án:
\(\dfrac{8}{3}\)
Giải thích các bước giải:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to - 1} \dfrac{{{x^2} + 10x + 9}}{{{x^4} + 2{x^3} - {x^2} - x + 1}}\\
= \mathop {\lim }\limits_{x \to - 1} \dfrac{{\left( {x + 1} \right)\left( {x + 9} \right)}}{{\left( {x + 1} \right)\left( {{x^3} + {x^2} - 2x + 1} \right)}}\\
= \mathop {\lim }\limits_{x \to - 1} \dfrac{{x + 9}}{{{x^3} + {x^2} - 2x + 1}}\\
= \dfrac{{ - 1 + 9}}{{{{\left( { - 1} \right)}^3} + {{\left( { - 1} \right)}^2} - 2.\left( { - 1} \right) + 1}} = \dfrac{8}{3}
\end{array}\)
