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[latex]\frac{5}{1+\sqrt{6}}+\frac{5}{\sqrt{6}+\sqrt{11}}+\frac{5}{\sqrt{11}+4}=[/latex] [latex]\frac{5(\sqrt{6}-1)}{(\sqrt{6}+1)(\sqrt{6}-1)}+\frac{5(\sqrt{11}-\sqrt{6})}{(\sqrt{11}+\sqrt{6})(\sqrt{11}-\sqrt{6})}+\frac{5(4-\sqrt{11})}{(4+\sqrt{11})(4-\sqrt{11})}=[/latex][latex]\frac{5(\sqrt{6}-1)}{(\sqrt{6})^2-1^2}+\frac{5(\sqrt{11}-\sqrt{6})}{(\sqrt{11})^2-(\sqrt{6})^2}+\frac{5(4-\sqrt{11})}{4^2-(\sqrt{11})^2}=[/latex] [latex]\frac{5(\sqrt{6}-1)}{6-1}+\frac{5(\sqrt{11}-\sqrt{6})}{11-6}+\frac{5(4-\sqrt{11})}{16-11}=[/latex] [latex]\sqrt{6}-1+\sqrt{11}-\sqrt{6}+4-\sqrt{11}=4-1=3[/latex] ответ: 3