If 7 - 2 7 + 2 = a 7 + b , then the value of a is?

Answer: Option B

$$\begin{array}{rl}& \frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b\\ & \text{L}\text{.H}\text{.S }\frac{\sqrt{7}-2}{\sqrt{7}+2}\times \frac{\sqrt{7}-2}{\sqrt{7}-2}\\ & \left(\text{Rationalisation}\right)\\ & =\frac{{\left(\sqrt{7}-2\right)}^2}{{\left(\sqrt{7}\right)}^2-\left(4\right)}\\ & =\frac{7+4-4\sqrt{7}}{7-4}\\ & =\frac{11-4\sqrt{7}}{3}\\ & =\frac{11}{3}-\frac{4}{3}\sqrt{7}\\ & =-\frac{4}{3}\sqrt{7}+\frac{11}{3}\\ & =a\sqrt{7}+b\left(\text{ R}\text{.H}\text{.S}\text{.}\right)\end{array}$$
(Compare the coefficients of $$\sqrt{7}$$ and constant term)
$$\begin{array}{rl}& \text{a}=-\frac{4}{3}\\ & b=\frac{11}{3}\end{array}$$