Help plz !!!!

Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where A, B, C, and D are integers, D is positive, and B is not divisible by the square of any prime. If the greatest common divisor of A, C, and D is 1, find A+B+C+D.

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$\frac{5}{2+\sqrt{6}}\,=\,\frac{5}{2+\sqrt6}\cdot\frac{2-\sqrt6}{2-\sqrt6}\,=\,\frac{10-5\sqrt6}{4-6}\,=\,\frac{10-5\sqrt6}{-2} \,=\,\frac{5\sqrt6-10}{2}$

 

Now it is in the form  $\frac{A\sqrt{B}+C}{D}$   and...

 

A, B, C, and D  are integers

 

D  is positive

 

B  is not divisible by the square of any prime

 

the GCF of  A, C, and D  =  the GCF  of  5, -10, and 2  =  1

 

A + B + C + D  =  5 + 6 + -10 + 2  =  3