a) \(\dfrac{2}{\sqrt{10}-3}+\dfrac{2}{\sqrt{10}+3}=\dfrac{2\left(\sqrt{10}+3\right)+2\left(\sqrt{10}-3\right)}{\left(\sqrt{10}-3\right)\left(\sqrt{10}+3\right)}\)
\(=\dfrac{4\sqrt{10}}{1}=4\sqrt{10}\)
b) \(\dfrac{3-2\sqrt{3}}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}=\dfrac{\sqrt{3}-2}{1}-\dfrac{2}{\sqrt{3}-1}\)
\(=\sqrt{3}-2-\dfrac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=\sqrt{3}-2-\dfrac{2\left(\sqrt{3}+1\right)}{2}\)
\(=\sqrt{3}-2-\sqrt{3}-1=-3\)
c) \(\dfrac{3}{\sqrt{5}-2}+\dfrac{3}{\sqrt{5}+2}-\dfrac{5-\sqrt{5}}{\sqrt{5}-1}\)
\(=\dfrac{3\left(\sqrt{5}+2\right)+3\left(\sqrt{5}-2\right)}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}-\dfrac{\sqrt{5}\left(\sqrt{5}-1\right)}{\sqrt{5}-1}\)
\(=\dfrac{6\sqrt{5}}{1}-\sqrt{5}=5\sqrt{5}\)
d) \(\dfrac{4}{\sqrt{3}-1}-2\sqrt{\left(\sqrt{3}-1\right)^2}=\dfrac{4\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-2\left|\sqrt{3}-1\right|\)
\(=\dfrac{4\left(\sqrt{3}+1\right)}{2}-2\left(\sqrt{3}-1\right)=2\left(\sqrt{3}+1\right)-2\sqrt{3}+2=4\)
mấy câu dưới bạn làm tương tự
