Tính giới hạnLim căn {{x^2} + x + 2}  - 2 / x - 1

Tính giới hạn \(\mathop {\lim }\limits_{x \to 1} \frac{{\sqrt {{x^2} + x + 2}  - 2}}{{x - 1}}\)\( = \mathop {\lim }\limits_{x \to 1} \frac{{{x^2} + x + 2 - 4}}{{\left( {x - 1} \right)\left( {\sqrt {{x^2} + x + 2}  + 2} \right)}}\)\( = \mathop {\lim }\limits_{x \to 1} \frac{{\left( {x - 1} \right)\left( {x + 2} \right)}}{{\left( {x - 1} \right)\left( {\sqrt {{x^2} + x + 2}  + 2} \right)}}\)

\( = \mathop {\lim }\limits_{x \to 1} \frac{{x + 2}}{{\sqrt {{x^2} + x + 2}  + 2}}\)\( = \frac{3}{4}\)