Tính giá trị của a − b .

Ta có \(\mathop {\lim }\limits_{x \to 3} \frac{{x + 1 - \sqrt {5x + 1} }}{{x - \sqrt {4x - 3} }}\) = \(\mathop {\lim }\limits_{x \to 3} \frac{{\left[ {{{\left( {x + 1} \right)}^2} - \left( {5x + 1} \right)} \right]\left[ {x + \sqrt {4x - 3} } \right]}}{{\left[ {{x^2} - \left( {4x - 3} \right)} \right]\left[ {x + 1 + \sqrt {5x + 1} } \right]}}\)

\(\mathop { = \lim }\limits_{x \to 3} \frac{{\left( {{x^2} - 3x} \right)\left( {x + \sqrt {4x - 3} } \right)}}{{\left( {{x^2} - 4x + 3} \right)\left( {x + 1 + \sqrt {5x + 1} } \right)}}\)\(\mathop { = \lim }\limits_{x \to 3} \frac{{x\left( {x - 3} \right)\left( {x + \sqrt {4x - 3} } \right)}}{{\left( {x - 1} \right)\left( {x - 3} \right)\left( {x + 1 + \sqrt {5x + 1} } \right)}}\)

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

Do đó \(a = 9;b = 8\) nên \(a - b = 1\).

Đáp án: 1.