The value of 4 + 3 3 7 + 4 3 is?

Answer: Option A

$$\frac{4+3\sqrt{3}}{7+4\sqrt{3}}$$
(By rationalization of denominator)
$$\begin{array}{rl}& =\frac{4+3\sqrt{3}}{7+4\sqrt{3}}\times \frac{7-4\sqrt{3}}{7-4\sqrt{3}}\\ & =\frac{\left(4+3\sqrt{3}\right)\left(7-4\sqrt{3}\right)}{49-48}\end{array}$$