Consider the circles  $x^2+y^2+3\sqrt{2}\left(x+y\right)=0$  and  $x^2+y^2+5\sqrt{2}\left(x+y\right)=0$ . A third circle is drawn internally tangent to larger circle and externally tangent to smaller circle and tangent to their common diameter. If radius of such circle is $\frac{p}{q}$ (p & q are relatively prime), then value of p – q is