Tính lim(x -> 5) (3x^2 - 13x - 10)/(25 - x^2)

Ta có \(\mathop {\lim }\limits_{x \to 5} \frac{{3{x^2} - 13x - 10}}{{25 - {x^2}}}\)\( = \mathop {\lim }\limits_{x \to 5} \frac{{\left( {x - 5} \right)\left( {3x + 2} \right)}}{{ - \left( {x - 5} \right)\left( {x + 5} \right)}}\)\( = \mathop {\lim }\limits_{x \to 5} \frac{{3x + 2}}{{ - \left( {x + 5} \right)}}\)\[ = \frac{{3 \cdot 5 + 2}}{{ - \left( {5 + 5} \right)}} = - \frac{{17}}{{10}}\].