Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2 }}$. 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. Find the minimum possible value of $A+B+C+D$.

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

We have

so that

Rewrite 16 and 32 as powers of 2, then simplify:

So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation