Tìm giới hạn \(\mathop {\lim }\limits_{x \to 1} \dfrac{{{x^4} - 3{x^2} + 2}}{{{x^3} + 2x - 3}}\)

* Hướng dẫn giải

\(\begin{array}{l}\mathop {\lim }\limits_{x \to 1} \dfrac{{{x^4} - 3{x^2} + 2}}{{{x^3} + 2x - 3}}\\ = \mathop {\lim }\limits_{x \to 1} \dfrac{{(x + 1)(x - 1)({x^2} - 2)}}{{(x - 1)({x^2} + x + 3)}}\\ = \mathop {\lim }\limits_{x \to 1} \dfrac{{(x + 1)({x^2} - 2)}}{{({x^2} + x + 3)}}\\ = \dfrac{{2.( - 1)}}{5} = \dfrac{{ - 2}}{5}\end{array}\)