Toán Lớp 9: • Thực hiện phép tính: $\frac{8}{√11+√3}$ + $\frac{1}{2-√3}$ – $\frac{11+√11}{√11+~1}$

TRẢ LỜI

1. $\textit{Giải đáp + Lời giải và giải thích chi tiết:}$

   8/(\sqrt{11}+\sqrt{3})+1/(2-\sqrt{3})-(11+\sqrt{11})/(\sqrt{11}+1)

   =(8(\sqrt{11}-\sqrt{3}))/((\sqrt{11}+\sqrt{3})(\sqrt{11}-\sqrt{3}))+(1(2+\sqrt{3}))/((2-\sqrt{3})(2+\sqrt{3}))-(\sqrt{11}(\sqrt{11}+1))/(\sqrt{11}+1)

   =(8(\sqrt{11}-\sqrt{3}))/((\sqrt{11})^2-(\sqrt{3})^2)+(2+\sqrt{3})/(2^2-(\sqrt{3)^2)-\sqrt{11}

   =\sqrt{11} -\sqrt{3}+2+\sqrt{3}-\sqrt{11}

   =2

   Trả lời
2. $\text{$\dfrac{8}{\sqrt{11}+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}-\dfrac{11+\sqrt{11}}{\sqrt{11}+1}$}$

   $\text{= $\dfrac{8(\sqrt{11}-\sqrt{3})}{(\sqrt{11})²-(\sqrt{3})²}+\dfrac{2+\sqrt{3}}{2²-(\sqrt{3})²}-\dfrac{\sqrt{11}(\sqrt{11}+1)}{\sqrt{11}+1}$}$

   $\text{= $\dfrac{8(\sqrt{11}-\sqrt{3})}{11-3}+\dfrac{2+\sqrt{3}}{4-3}-\sqrt{11}$}$

   $\text{= $\dfrac{8(\sqrt{11}-\sqrt{3})}{8}+2+\sqrt{3}-\sqrt{11}$}$

   $\text{= $\sqrt{11}-\sqrt{3}+2+\sqrt{3}-\sqrt{11}=2$}$

   Trả lời