question_answer

If both a and b are rational numbers, find the value of a and b in equation: \[\left( \frac{3+\sqrt{5}}{3-\sqrt{5}}=a+b\sqrt{5} \right)\]

A) \[a=\frac{2}{7}\] and \[b=\frac{3}{2}\]

B) \[a=\frac{7}{2}\] and \[b=\frac{2}{3}\]

C) \[a=\frac{7}{2}\] and \[b=\frac{3}{2}\]

D) \[a=\frac{3}{7}\] and \[b=\frac{7}{3}\]

E) None of these