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) \(\frac{9-a}{\sqrt{a}+3}\)- \(\frac{9-6.\sqrt{a}+a}{\sqrt{a}-3}\)- 6
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
\(P=\frac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
rút gọn
a/ \(\frac{\sqrt{a}+\sqrt{b}}{2\sqrt{a}-2\sqrt{b}}-\frac{\sqrt{a}-\sqrt{b}}{2\sqrt{a}+2\sqrt{b}}-\frac{2b}{b-a}\)
CMR
\(A=\left(\frac{\sqrt{x}}{3+x}+\frac{x+9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)
\(A=\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
a) Rút gọn
b) Tìm x để A < 1
RÚT GỌN CÁC BIỂU THỨC SAU
\(A=\frac{-2}{3}\sqrt{\frac{\left(a-b\right)^3.b^5}{c}}.\frac{9}{4}\sqrt{\frac{c^3}{2\left(a-b\right)}}.\sqrt{98b}\)
\(B=\left(\sqrt{ab}+2\sqrt{\frac{b}{a}}-\sqrt{\frac{a}{b}+\sqrt{\frac{1}{ab}}}\right).\sqrt{ab}\)
Bài 1: Tìm điều kiện xác đinh của các biểu thức sau
a, A=\(\frac{x-1}{\sqrt{x-1}}+\sqrt{2x+5}\)
b, B=\(\frac{\sqrt{-x}}{x^2-3}-2019\)
Bài 2: Rút gọn
a, A=\(\frac{15-9\sqrt{2}}{5\sqrt{5}-3\sqrt{10}}-\sqrt{\frac{16}{5}}-\frac{1}{\sqrt{10}+\sqrt{5}}\)
b, B=\(\frac{\sqrt{145\sqrt{154}}-\sqrt{9-\sqrt{77}}}{1-\frac{1}{\sqrt{2}}}\)