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