Cho hàm số \(f\left( x \right) = \frac{{\sqrt {{x^2} + 3{a^2}}  - 2a}}{{x - a}} + a\), (với \(a > 0,\,\,a\) là tham số).

A. \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{{2a - 1}}{2}.\)

B. \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{{2a + 1}}{2}.\)

C. \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{2}{{2a + 1}}.\)

D. \(\mathop {\lim }\limits_{x \to a} f\left( x \right) = \frac{2}{{2a - 1}}.\)