Rút gọn \(\frac{-x+5\sqrt{x}+4}{\left(\sqrt{x}-1\right)^2}\)
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Bài 1: Rút gọna. left(5-2sqrt{3}right)^2+left(5+2sqrt{3}right)^2b. left(sqrt{5}+sqrt{2}right)^2-left(2sqrt{5}+1right)left(2sqrt{5}-1right)-sqrt{40}c. left(sqrt{2}-1right)^2-frac{2}{3}sqrt{4}+frac{4sqrt{2}}{5}+sqrt{1frac{11}{15}}-sqrt{2}d. left(sqrt{6}-sqrt{18}+5sqrt{2}-frac{1}{2}sqrt{8}right)2sqrt{6}+2sqrt{3}e. left(2sqrt{3}-3sqrt{2}right)^2+6sqrt{6}+3sqrt{24}Bài 2: Rút gọnA left(frac{1}{x-sqrt{x}}+frac{1}{sqrt{x}-1}:frac{sqrt{x+1}}{x-2sqrt{x}+1}right)(x0 ; x khác 1)
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Bài 1: Rút gọn
a. \(\left(5-2\sqrt{3}\right)^2+\left(5+2\sqrt{3}\right)^2\)
b. \(\left(\sqrt{5}+\sqrt{2}\right)^2-\left(2\sqrt{5}+1\right)\left(2\sqrt{5}-1\right)-\sqrt{40}\)
c. \(\left(\sqrt{2}-1\right)^2-\frac{2}{3}\sqrt{4}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{15}}-\sqrt{2}\)
d. \(\left(\sqrt{6}-\sqrt{18}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right)2\sqrt{6}+2\sqrt{3}\)
e. \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+6\sqrt{6}+3\sqrt{24}\)
Bài 2: Rút gọn
A =\(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}:\frac{\sqrt{x+1}}{x-2\sqrt{x}+1}\right)\)(x>0 ; x khác 1)
cho biểu thức M=\(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(\frac{3\sqrt{x}-5}{\sqrt{x}-2}+\frac{2\sqrt{x}+10}{x+6\sqrt{x}+5}\right)\)
Rút gọn
Rút gọn biểu thức A = \(\left(1+\frac{5}{\sqrt{x}-2}\right).\left(\sqrt{x}-\frac{x+2\sqrt{x}+4}{\sqrt{x}+3}\right)\)
\(A=\left(1+\frac{5}{\sqrt{x}-2}\right).\left(\sqrt{x}-\frac{x+2\sqrt{x}+4}{\sqrt{x}+3}\right).\)
\(=\frac{\sqrt{x}-2+5}{\sqrt{x}-2}.\frac{x+3\sqrt{x}-x-2\sqrt{x}-4}{\sqrt{x}+3}\)
\(=\frac{\sqrt{x}+3}{\sqrt{x}-2}.\frac{\sqrt{x}-4}{\sqrt{x}+3}=\frac{\sqrt{x}-4}{\sqrt{x}-2}\)
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Nhờ các bạn rút gọn.
\(A=\frac{\sqrt{x+\sqrt{4\left(x-1\right)}}-\sqrt{x-\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(\sqrt{x-1}-\frac{1}{\sqrt{x-1}}\right)\)
A = \(\frac{2}{\sqrt{x-1}}\)
Rút gọn B=\(\left(\frac{1}{\sqrt{x}-2}-\frac{2}{\sqrt{x}+2}+\frac{x}{x\sqrt{x}-4\sqrt{x}}\right):\left(\frac{6-x}{\sqrt{x}+2}+2+\sqrt{x}\right)\)
\(B=\left(\frac{1}{\sqrt{x}-2}-\frac{2}{\sqrt{x}+2}+\frac{x}{x\sqrt{x}-4\sqrt{x}}\right):\left(\frac{6-x}{\sqrt{x}+2}+2+\sqrt{x}\right)\)
\(B=\left(\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x+2}\right)}\right):\left(\frac{6-x+2\left(\sqrt{x}+2\right)+\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\right)\)
\(B=\left(\frac{\sqrt{x}+2-2\sqrt{x}+4+\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(\frac{6-x+2\sqrt{x}+4+x+2\sqrt{x}}{\sqrt{x}+2}\right)\)
\(B=\frac{6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\frac{\sqrt{x}+2}{10+4\sqrt{x}}\)
\(B=\frac{6}{\sqrt{x}-2}\cdot\frac{1}{2\left(5+2\sqrt{x}\right)}\)
B = \(\frac{3}{\left(\sqrt{x}-2\right)\left(5+2\sqrt{x}\right)}\)
Rút gọn biểu thức Q =\(\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\left(1-\frac{1}{x-1}\right)\)
Rút gọn A=\(\frac{\sqrt{x-\sqrt{4x-4}}+\sqrt{x+4\sqrt{4x-4}}}{\sqrt{x^2-4\left(x-1\right)}}.\left(1-\frac{1}{x-1}\right)\)
a,Cho biểu thức:\(M=\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right):\left(\frac{3\sqrt{x}-5}{\sqrt{x}-2}+\frac{2\sqrt{x}+10}{x+6\sqrt{x}5}\right)\)
Rút gọn M và tìm x để M>1
rút gọn
M=\(\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\).\(\left(1-\frac{1}{x-1}\right)\)
\(M=\frac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\cdot\left(1-\frac{1}{x-1}\right)\)
\(M=\frac{\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}}{\sqrt{x^2-4x+4}}\cdot\frac{x-1-1}{x-1}\)
\(M=\frac{\sqrt{\left(\sqrt{x-1}-1\right)^2}+\sqrt{\left(\sqrt{x-1}+1\right)^2}}{\sqrt{\left(x-2\right)^2}}\cdot\frac{x-2}{x-1}\) (đk: \(x\ge1\)
\(M=\frac{\left|\sqrt{x-1}-1\right|+\left|\sqrt{x-1}+1\right|}{\left|x-2\right|}\cdot\frac{x-2}{x-1}\)
Nếu \(1\le x< 2\) =>\(M=\frac{1-\sqrt{x-1}+\sqrt{x-1}+1}{2-x}\cdot\frac{x-2}{x-1}\)
\(M=-\frac{2}{x-1}\)
Nếu x > 2 => \(M=\frac{\sqrt{x-1}-1+\sqrt{x-1}+1}{x-2}\cdot\frac{x-2}{x-1}\)
\(\frac{2\sqrt{x-1}}{x-1}=\frac{2}{\sqrt{x-1}}\)
Cho biểu thức: \(P=\left(\frac{\sqrt{x}-3}{2-\sqrt{x}}+\frac{\sqrt{x}+2}{3+\sqrt{x}}-\frac{9-x}{x+\sqrt{x}-6}\right):\left(1-\frac{3\sqrt{x}-9}{x-9}\right)\)
a)Rút gọn biểu thức
b)Tính P với \(x=\frac{\sqrt{4+2\sqrt{3}}\left(\sqrt{x}-1\right)}{\sqrt{6+2\sqrt{5}-\sqrt{5}}}\)
Mình ghi nhầm. \(x=\frac{\sqrt{4+2\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-\sqrt{5}}\)nhé