question_answer

If \[\frac{5-\sqrt{6}}{5+\sqrt{6}}=p+q\sqrt{6},\] then which one of the following options represents the value of p and q?

A)  \[p\,=\frac{31}{19},q=\frac{10}{19}\]  

B)  \[p=-\frac{31}{19},q=\frac{10}{19}\]

C)  \[p=-\frac{31}{19},q=-\frac{10}{19}\]  

D)  \[p=\frac{31}{19},q=-\frac{10}{19}\]

E)  None of these