Hãy rút gọn các biểu thức sau: a) D = \(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{4x}{x-1}\)
b) E = \(\dfrac{\sqrt{x}+1}{x-\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}+\dfrac{5x-8\sqrt{x}+5}{x\sqrt{x}+1}\)
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Rút gọn các biểu thức sau:Aleft(dfrac{1}{sqrt{a}+2}+dfrac{1}{sqrt{a}-2}right):dfrac{sqrt{a}}{a-4}Bleft(dfrac{4x}{sqrt{x}-1}-dfrac{sqrt{x}-2}{x-3sqrt{x}+2}right).dfrac{sqrt{x}-1}{x^2}Cleft(dfrac{1}{sqrt{x}+3}+dfrac{2sqrt{x}}{x-9}right).dfrac{2sqrt{x}+6}{sqrt{x}-1}Dleft(dfrac{5sqrt{x}-6}{x-9}-dfrac{2}{sqrt{x}+3}right):left(1+dfrac{6}{x-9}right)Eleft(dfrac{sqrt{x}}{3+sqrt{x}}+dfrac{9+x}{9-x}right).left(3sqrt{x}-xright) help
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Rút gọn các biểu thức sau:
\(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right).\dfrac{\sqrt{x}-1}{x^2}\)
\(C=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{x-9}\right).\dfrac{2\sqrt{x}+6}{\sqrt{x}-1}\)
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(E=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
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Rút gọn các biểu thức sau:Aleft(dfrac{1}{sqrt{a}+2}+dfrac{1}{sqrt{a}-2}right):dfrac{sqrt{a}}{a-4}Bleft(dfrac{4x}{sqrt{x}-1}-dfrac{sqrt{x}-2}{x-3sqrt{x}+2}right).dfrac{sqrt{x}-1}{x^2}Cleft(dfrac{1}{sqrt{x}+3}+dfrac{2sqrt{x}}{x-9}right).dfrac{2sqrt{x}+6}{sqrt{x}-1}Dleft(dfrac{5sqrt{x}-6}{x-9}-dfrac{2}{sqrt{x}+3}right):left(1+dfrac{6}{x-9}right)Eleft(dfrac{sqrt{x}}{3+sqrt{x}}+dfrac{9+x}{9-x}right).left(3sqrt{x}-xright) help
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Rút gọn các biểu thức sau:
\(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right).\dfrac{\sqrt{x}-1}{x^2}\)
\(C=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{x-9}\right).\dfrac{2\sqrt{x}+6}{\sqrt{x}-1}\)
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(E=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
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a) Ta có: \(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(=\dfrac{\sqrt{a}-2+\sqrt{a}+2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}{\sqrt{a}}\)
=2
b) Ta có: \(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right)\cdot\dfrac{\sqrt{x}-1}{x^2}\)
\(=\dfrac{4x-1}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}-1}{x^2}\)
\(=\dfrac{4x-1}{x^2}\)
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Rút gọn các biểu thức sau:Cleft(dfrac{sqrt{a}}{sqrt{a}-1}-dfrac{sqrt{a}}{a-sqrt{1}}right):dfrac{sqrt{a}+1}{a-1}Dleft(dfrac{x-2}{x+2sqrt{x}}+dfrac{1}{sqrt{x}+2}right).dfrac{sqrt{x}+1}{sqrt{x}-1}Eleft(1+dfrac{x+sqrt{x}}{sqrt{x}+1}right)left(1+dfrac{x-sqrt{x}}{1-sqrt{x}}right)Làm ơn giúp mình với ạ!!mình đang cần gấp lắm!!
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Rút gọn các biểu thức sau:
\(C=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{1}}\right):\dfrac{\sqrt{a}+1}{a-1}\)
\(D=\left(\dfrac{x-2}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}+2}\right).\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(E=\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\)
Làm ơn giúp mình với ạ!!mình đang cần gấp lắm!!
A=\(1-\left(\dfrac{2}{1+2\sqrt{x}}-\dfrac{5\sqrt{x}}{4x-1}-\dfrac{1}{1-2\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{4x+4\sqrt{x}+1}\)
Rút gọn biểu thức trên
\(A=1-\left(\dfrac{2}{1+2\sqrt{x}}-\dfrac{5\sqrt{x}}{4x-1}-\dfrac{1}{1-2\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{4x+4\sqrt{x}+1}\)
\(A=1-\dfrac{2\left(2\sqrt{x}-1\right)-5\sqrt{x}+\left(2\sqrt{x}+1\right)}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}:\dfrac{\sqrt{x}-1}{\left(2\sqrt{x}+1\right)^2}\)
\(A=1-\dfrac{4\sqrt{x}-2-5\sqrt{x}+2\sqrt{x}+1}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}\cdot\dfrac{\left(2\sqrt{x}+1\right)^2}{\sqrt{x}-1}\)
\(A=1-\dfrac{\sqrt{x}-1}{\left(2\sqrt{x}-1\right)\left(2\sqrt{x}+1\right)}\cdot\dfrac{\left(2\sqrt{x}+1\right)^2}{\sqrt{x}-1}\)
\(A=1-\dfrac{2\sqrt{x}+1}{2\sqrt{x}-1}=\dfrac{2\sqrt{x}-1-2\sqrt{x}-1}{2\sqrt{x}-1}=\dfrac{-2}{2\sqrt{x}-1}\)
Tick hộ nha
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5 tháng 9 2023 lúc 19:47
RÚT GỌN CÁC BIỂU THỨC SAU:21) A left(dfrac{xsqrt{x} + 1}{x - 1} - dfrac{x - 1}{sqrt{x} - 1}right) : left(sqrt{x} + dfrac{sqrt{x}}{sqrt{x} - 1}right) 22) A left(dfrac{x}{sqrt{x} - 1} - sqrt{x}right) : left(dfrac{sqrt{x} + 1}{sqrt{x}} - dfrac{1}{1 - sqrt{x}} + dfrac{2 - x}{x - sqrt{x}}right)23) A left(dfrac{sqrt{x} - 4}{x - 2sqrt{x}} - dfrac{3}{2 - sqrt{x}}right) : left(dfrac{sqrt{x} + 2}{sqrt{x}} - dfrac{sqrt{x}}{sqrt{x} - 2}right)24) A left(dfrac{2x + 1}{xsqrt{x} - 1} + dfrac{1}{1 - sqrt{x}}...
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RÚT GỌN CÁC BIỂU THỨC SAU:
21) \(A = \left(\dfrac{x\sqrt{x} + 1}{x - 1} - \dfrac{x - 1}{\sqrt{x} - 1}\right) : \left(\sqrt{x} + \dfrac{\sqrt{x}}{\sqrt{x} - 1}\right) \)
22) \(A = \left(\dfrac{x}{\sqrt{x} - 1} - \sqrt{x}\right) : \left(\dfrac{\sqrt{x} + 1}{\sqrt{x}} - \dfrac{1}{1 - \sqrt{x}} + \dfrac{2 - x}{x - \sqrt{x}}\right)\)
23) \(A = \left(\dfrac{\sqrt{x} - 4}{x - 2\sqrt{x}} - \dfrac{3}{2 - \sqrt{x}}\right) : \left(\dfrac{\sqrt{x} + 2}{\sqrt{x}} - \dfrac{\sqrt{x}}{\sqrt{x} - 2}\right)\)
24) \(A = \left(\dfrac{2x + 1}{x\sqrt{x} - 1} + \dfrac{1}{1 - \sqrt{x}}\right) : \left(1 - \dfrac{x - 2}{x + \sqrt{x} + 1}\right)\)
25) \(A = 1 : \left(\dfrac{x + 2\sqrt{x} - 2}{x\sqrt{x} + 1} - \dfrac{\sqrt{x} -1}{x - \sqrt{x} + 1} + \dfrac{1}{\sqrt{x} + 1}\right)\)
26) \(A = \left(\dfrac{\sqrt{x}}{\sqrt{x} + 2} - \dfrac{3}{2 - \sqrt{x}} + \dfrac{3\sqrt{x} - 2}{x - 2}\right) : \left(\dfrac{\sqrt{x} + 3}{\sqrt{x} - 2} + \dfrac{2\sqrt{x}}{2\sqrt{x} - x}\right)\)
27) \(P = \left(\dfrac{4\sqrt{x}}{2 + \sqrt{x}} + \dfrac{8}{4 - x}\right) : \left(\dfrac{\sqrt{x} - 1}{x - 2\sqrt{x}} - \dfrac{2}{\sqrt{x}}\right)\)
21: ĐKXĐ: x>0; x<>1
\(A=\left(\dfrac{x\sqrt{x}+1-\left(x-1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right):\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)+\sqrt{x}}{\sqrt{x}-1}\)
\(=\dfrac{x\sqrt{x}+1-x\sqrt{x}-x+\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}-1}{x}\)
\(=\dfrac{-x+\sqrt{x}+2}{\sqrt{x}+1}\cdot\dfrac{1}{x}\)
\(=\dfrac{-\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}{x\left(\sqrt{x}+1\right)}=\dfrac{-\sqrt{x}+2}{x}\)
22:
DKXĐ: x>0; x<>1
\(A=\dfrac{x-\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}:\left(\dfrac{\sqrt{x}+1}{\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}+\dfrac{2-x}{\sqrt{x}\left(\sqrt{x}-1\right)}\right)\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-1}:\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)+\sqrt{x}+2-x}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{x-1+\sqrt{x}+2-x}\)
\(=\dfrac{x}{\sqrt{x}+1}\)
23: ĐKXĐ: x>0; x<>4
\(A=\dfrac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}:\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-x}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{-4}\)
\(=\dfrac{-4\sqrt{x}+4}{4}=-\sqrt{x}+1\)
24: ĐKXĐ: x>=0; x<>1
\(A=\dfrac{2x+1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}:\dfrac{x+\sqrt{x}+1-x+2}{x+\sqrt{x}+1}\)
\(=\dfrac{x-\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{\sqrt{x}+3}\)
\(=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
25:
ĐKXĐ: x>=0; x<>1
\(A=1:\dfrac{x+2\sqrt{x}-2-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+x-\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{2x+\sqrt{x}-1-x+1}\)
\(=\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{x+\sqrt{x}}=\dfrac{x-\sqrt{x}+1}{\sqrt{x}}\)
27: ĐKXĐ: x>0; x<>4
\(P=\dfrac{4\sqrt{x}\left(\sqrt{x}-2\right)-8}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\dfrac{\sqrt{x}-1-2\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{4x-8\sqrt{x}-8}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-1-2\sqrt{x}+1}\)
\(=\dfrac{4\left(x-2\sqrt{x}-2\right)}{\sqrt{x}+2}\cdot\dfrac{\sqrt{x}}{-\sqrt{x}}\)
\(=\dfrac{-4\left(x-2\sqrt{x}-2\right)}{\sqrt{x}+2}\)
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5 tháng 8 2021 lúc 8:44
Rút gọn các biểu thức sau:
1.\(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
2.\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
5 tháng 8 2021 lúc 13:20
Rút gọn các biểu thức sau:
1.\(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
2.\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
1: Ta có: \(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\dfrac{x+\sqrt{x}+1-x-2-x+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-x+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{-\sqrt{x}}{x+\sqrt{x}+1}\)
2) Ta có: \(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
\(=-\left(\dfrac{\sqrt{x}+1}{x-1}-\dfrac{x+2}{x\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}\right)\)
\(=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)
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2 a. rút gọn biểu C = \(\dfrac{2x^{\text{2}}-x}{\text{x }-1}+\dfrac{x+1}{1-x}+\dfrac{2-x^2}{x-1}\)
b. Rút gọn biểu thức D = \(\left(\dfrac{1}{a-\sqrt{a}}+\dfrac{1}{\sqrt{\text{a}}-1}\right):\dfrac{\sqrt{\text{a}}+1}{a-2\sqrt{a}+1}\)
Vậy khi rút gọn một biểu thức hửu tỉ và một biểu thức chứa căn có tìm điều kiện xác định không?
\(a,C=\dfrac{2x^2-x-x-1+2-x^2}{x-1}\left(x\ne1\right)\\ C=\dfrac{x^2-2x+1}{x-1}=\dfrac{\left(x-1\right)^2}{x-1}=x-1\\ b,D=\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\left(a>0;a\ne1\right)\\ D=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)
Có
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11 tháng 10 2023 lúc 18:17
1) Tính giá trị của biểu thức : A= 3\(\sqrt{\dfrac{1}{3}}\) - \(\dfrac{5}{2}\)\(\sqrt{12}\) - \(\sqrt{48}\)
2) Tìm x để biểu thức sau có nghĩa : A=\(\sqrt{12-4x}\)
3) Rút gọn biểu thức : P= \(\dfrac{2x-2\sqrt{x}}{x-1}\) với x≥0 và x ≠1
1) \(A=3\sqrt{\dfrac{1}{3}}-\dfrac{5}{2}\sqrt{12}-\sqrt{48}\)
\(=3\cdot\dfrac{\sqrt{1}}{\sqrt{3}}-\dfrac{5\sqrt{12}}{2}-\sqrt{4^2\cdot3}\)
\(=\dfrac{3\cdot1}{\sqrt{3}}-\dfrac{5\cdot2\sqrt{3}}{2}-4\sqrt{3}\)
\(=\sqrt{3}-5\sqrt{3}-4\sqrt{3}\)
\(=-8\sqrt{3}\)
2) \(A=\sqrt{12-4x}\) có nghĩa khi:
\(12-4x\ge0\)
\(\Leftrightarrow4x\le12\)
\(\Leftrightarrow x\le\dfrac{12}{4}\)
\(\Leftrightarrow x\le3\)
3) \(\dfrac{2x-2\sqrt{x}}{x-1}\)
\(=\dfrac{2\sqrt{x}\cdot\sqrt{x}-2\sqrt{x}}{\left(\sqrt{x}\right)^2-1^2}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{2\sqrt{\text{x}}}{\sqrt{x}+1}\)
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Cho biểu thức: \(A=\dfrac{\sqrt{x}-1}{2\sqrt{x}+1}-\dfrac{3}{1-2\sqrt{x}}-\dfrac{4\sqrt{x}+4}{4x-1}\) và \(B=\dfrac{\sqrt{x}-4}{\sqrt{x}}\)với x > 0 , x = 1/4
a. TÍnh giá trị của biểu thức B biết \(x=\sqrt{28-16\sqrt{3}}+2\sqrt{3}\)
b. Rút gọn biểu thức A
a: Ta có: \(x=\sqrt{28-16\sqrt{3}}+2\sqrt{3}\)
\(=4-2\sqrt{3}+2\sqrt{3}\)
=4
Thay x=4 vào B, ta được:
\(B=\dfrac{2-4}{2}=-1\)
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