1, trục căn thức ỏ mẫu:
\(a,\frac{2+\sqrt{3}}{2-\sqrt{3}}\) \(b,\frac{1}{\sqrt{x}+\sqrt{y}}\) \(c,\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}\)
\(d,\frac{1}{\sqrt{3}+\sqrt{2}+1}\) \(e,\frac{1}{\sqrt{3}-\sqrt{3}+2}\)
2. tính
\(a,\frac{\sqrt{45}-\sqrt{2}}{\sqrt{5-\sqrt{2}}}\) b, \(\frac{\sqrt{3}+1}{\sqrt{3}-1}+\frac{\sqrt{3-1}}{\sqrt{3}+1}\) c,\(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
Bài 2 : Sửa đề phần a;b
a,\(\frac{\sqrt{45}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}=\frac{3\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}=\frac{13+2\sqrt{10}}{3}\)
b, \(\frac{\sqrt{3}+1}{\sqrt{3}-1}+\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{\left(\sqrt{3}+1\right)^2\left(\sqrt{3}-1\right)^2}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)=2\)
c, \(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}=\frac{2\left(\sqrt{3}+1\right)-2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}=\frac{4}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
B1:
a) \(\frac{2+\sqrt{3}}{2-\sqrt{3}}=\frac{\left(2+\sqrt{3}\right)^2}{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}=\frac{7+4\sqrt{3}}{4-3}=7+4\sqrt{3}\)
b) \(\frac{1}{\sqrt{x}+\sqrt{y}}=\frac{\sqrt{x}-\sqrt{y}}{x-y}\)
c) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}=\frac{\left(\sqrt{5}-\sqrt{3}\right)\sqrt{2}}{2}=\frac{\sqrt{10}-\sqrt{6}}{2}\)
d) \(\frac{1}{\sqrt{3}+\sqrt{2}+1}=\frac{\sqrt{3}+\sqrt{2}-1}{\left(\sqrt{3}+\sqrt{2}\right)^2-1}=\frac{\sqrt{3}+\sqrt{2}-1}{4+2\sqrt{6}}\)
\(=\frac{\left(\sqrt{3}+\sqrt{2}-1\right)\left(2-\sqrt{6}\right)}{2\left(4-6\right)}=\frac{2+\sqrt{2}-\sqrt{6}}{4}\)
e) \(\frac{1}{\sqrt{3}-\sqrt{3}+2}=\frac{1}{2}\)