Giới hạn \(\mathop {\lim }\limits_{x \to 3} \frac{{x + 1 - \sqrt {5x + 1} }}{{x - \sqrt {4x - 3} }}\) bằng \(\frac{a}{b}\) (phân số

* Hướng dẫn giải

Ta có \(\mathop {\lim }\limits_{x \to 3} \frac{{x + 1 - \sqrt {5x + 1} }}{{x - \sqrt {4x - 3} }} = \mathop {\lim }\limits_{x \to 3} \frac{{\left( {x + \sqrt {4x - 3} } \right)\left( {x - 3} \right)x}}{{\left( {x + 1 + \sqrt {5x + 1} } \right)\left( {x - 3} \right)\left( {x - 1} \right)}} = \mathop {\lim }\limits_{x \to 3} \frac{{x\left( {x + \sqrt {4x - 3} } \right)}}{{\left( {x - 1} \right)\left( {x + 1 + \sqrt {5x + 1} } \right)}} = \frac{9}{8}\)

Suy ra \(a = 9;\,\,b = 8 \Rightarrow a - b = 1\)