In the following determine rational numbers a and b: $$\dfrac{5+3\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$$
Correct option is B. $$ a = -1, b = -1$$
Given,
$$\dfrac{5+3\sqrt{3}}{7+4\sqrt{3}}$$
$$=\dfrac{\left(5+3\sqrt{3}\right)\left(7-4\sqrt{3}\right)}{\left(7+4\sqrt{3}\right)\left(7-4\sqrt{3}\right)}$$
$$=\dfrac{\sqrt{3}-1}{1}$$
$$=-1+\sqrt 3$$
$$=a+b\sqrt 3$$
upon comparision, we get,
$$a=-1,b=1$$