Câu 1 : Rút gọn biểu thức
a, \(\frac{2}{5}\sqrt{75}-0,5\sqrt{48}+\sqrt{300}-\frac{2}{3}\sqrt{12}.\)b, \(\frac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\frac{3}{3+3\sqrt{6}}.\)
c\(\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}.\)Với a>0;b>0
Rút gọn
a) ( 2 - \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\) ) . (2 - \(\frac{5-\sqrt{a}-\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)
Rút gọn
a) ( 2 - \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\) ) . (2 - \(\frac{5-\sqrt{a}-\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)
Rút gọn
a) ( 2 - \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\) ) . (2 - \(\frac{5-\sqrt{a}-\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)
Rut gon
a) ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\)) . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
Rut gon
a) ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\)) . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
Rut gon
a) ( 2- \(\frac{a-3.\sqrt{a}}{\sqrt{a}-3}\)) . ( 2- \(\frac{5.\sqrt{a}+\sqrt{a}.b}{\sqrt{b}-5}\))
b) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
Giúp mình làm bài này với
Bài 1: Tính
A=\(\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}+\sqrt{\frac{5-2\sqrt{6}}{5+2\sqrt{6}}}\)
B=\(\frac{\sqrt{2+\sqrt{3}}}{2}\div\left(\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}\right)\)
C=\(\frac{1}{\sqrt{2}+2}+\frac{1}{2\sqrt{3}+3\sqrt{2}}+...+\frac{1}{99\sqrt{100}+100\sqrt{99}}\)
Bài 2: Giải phương trình:
a. \(\sqrt{4x-20}+\sqrt{x-5}-\frac{1}{3}\sqrt{9x-45}=4\)
b.\(\frac{2\sqrt{x}-7}{3}=\sqrt{x}-1\)
c.\(5\sqrt{x-1}-\sqrt{36x-36}-\sqrt{9x-9}=\sqrt{8x+12}\)
Bài 3: Rút gọn
\(M=\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\times\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a-1}}\right)\)
a. Tìm a để M>0
b. Tìm a để M<0
Bài 1:Rút gọn
\(a,\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
\(b,\frac{2}{5-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)
\(c,\left(1+\frac{a+\sqrt{a}}{1+\sqrt{a}}\right)\times\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)+a\left(a\ne1;a\ge0\right)\)
Bài 2: Rút gọn biểu thức
\(P=\frac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)