[tex]\sqrt{(x+y+z)+2\sqrt{xz+yz}}-\sqrt{(x+y+z)-2\sqrt{xz+yz}} \\=\sqrt{x+y+z+2\sqrt{z(x+y)}+z}-\sqrt{x+y-2\sqrt{z(x+y)+z}} \\=\sqrt{(\sqrt{x+y}+\sqrt{z})^2}-\sqrt{(\sqrt{x+y}-\sqrt{z})^2} \\=\sqrt{x+y}+\sqrt{z}-\sqrt{x+y}+\sqrt{z}(x+y>z) \\=2 \sqrt{z}[/tex]