Two positive numbers and have the property that their sum is equal to their product. If their difference is 7, what is \(\frac{1}{\frac{1}{p^2}+\frac{1}{q^2}}\)? Your answer will be of the form \(\frac{a+b\sqrt{c}}{d}\), where a and b don't both share a common factor with d and c has no square as a factor. Find a+b+c+d.
