\(\sqrt{12-2\sqrt{11}}-\sqrt{12+2\sqrt{11}}\\ =\sqrt{11-2\cdot1\cdot\sqrt{11}+1}-\sqrt{11+2\cdot1\cdot\sqrt{11}+1}\\ =\sqrt{\left(\sqrt{11}\right)^2-2\cdot1\cdot\sqrt{11}+1^2}-\sqrt{\left(\sqrt{11}\right)^2+2\cdot1\cdot\sqrt{11}+1^2}\\ =\sqrt{\left(\sqrt{11}-1\right)^2}-\sqrt{\left(\sqrt{11}+1\right)^2}\\ =\sqrt{11}-1-\sqrt{11}-1\\ =-2\)
\(\sqrt{12-2\sqrt{11}}-\sqrt{12+2\sqrt{11}}\)
\(=\sqrt{11-2\sqrt{11}\cdot1+1}-\sqrt{11+2\sqrt{11}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{11}-1\right)^2}-\sqrt{\left(\sqrt{11}+1\right)^2}\)
\(=\sqrt{11}-1-\sqrt{11}-1\)
\(=-2\)
