Hey I tryied playing with it,

here is what I ended with

(abc)^(1/2)*[c*(a+b)*[a^[1/2]/(a+c)-b^[1/2]/(c+b)]- a*(b+c)*[b^[1/2]/(a+b)-c^[1/2]/(c+a)]+ b*(c+a)*[c^[1/2]/(c+b)-a^[1/2]/(b+a)]]

I couldn't make it look all good in latex, but it look great on matlab or wolfram =)

(abc)^(1/2)*[c*(a+b)*[a^[1/2]/(a+c)-b^[1/2]/(c+b)]- a*(b+c)*[b^[1/2]/(a+b&

I tryied some rule I know with determinant, nothing helped me.

Hope it helped