Rút gọn B=\(\left(\frac{3x +3\sqrt{x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}+1}+\frac{1}{\sqrt{x}+2}-2\right):\frac{1}{x-1}\)
Những câu hỏi liên quan
Rút gọn1.Aleft(frac{2sqrt{x}}{sqrt{x}+3}+frac{sqrt{x}}{sqrt{x}-3}-frac{3x+3}{x-9}right):left(frac{2sqrt{x}-2}{sqrt{x}-3}-1right)2.Bleft(frac{sqrt{a}+1}{sqrt{ab}+1}+frac{sqrt{ab}+sqrt{a}}{sqrt{ab}-1}-1right):left(frac{sqrt{a}+1}{sqrt{ab}+1}-frac{sqrt{ab}+sqrt{a}}{sqrt{ab}-1}+1right)3.Cleft(frac{2x-1+sqrt{x}}{1-x}+frac{2xsqrt{x}+x-sqrt{x}}{1+xsqrt{x}}right).left(frac{left(x-sqrt{x}right)left(1-sqrt{x}right)}{2sqrt{x}-1}right)
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Rút gọn
\(1.A=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(2.B=\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}+\frac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}-1\right):\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}-\frac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}+1\right)\)
\(3.C=\left(\frac{2x-1+\sqrt{x}}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right).\left(\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right)\)
Bài 1
C=\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}+\frac{3x+3}{9-x}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}-3}-\frac{1}{2}\right)\)
a,Rút gọn
b,tìm x để C=\(\frac{1}{2}\)
\(C=\left(\frac{2\sqrt{x}}{\sqrt{x}-3}+\frac{\sqrt{x}}{\sqrt{x}-3}+\frac{3x+3}{9-x}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}-3}-\frac{1}{2}\right)\) ĐK \(x\ge0;x\ne9\)
\(C=\left(\frac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x+3}\right)}-\frac{3x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\frac{2\left(\sqrt{x}-1\right)}{2\left(\sqrt{x}-3\right)}-\frac{1\left(\sqrt{x}-3\right)}{2\left(\sqrt{x}-3\right)}\right)\)
\(C=\frac{2x-6\sqrt{x}+x+3\sqrt{x}-3x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}:\left(\frac{2\sqrt{x}-2-\sqrt{x}+3}{2\left(\sqrt{x}-3\right)}\right)\)
\(C=\frac{-3\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}:\frac{\sqrt{x}+1}{2\left(\sqrt{x}-3\right)}\)
\(C=\frac{-3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\) x \(\frac{2\left(\sqrt{x}-3\right)}{\sqrt{x}+1}\)
\(C=\frac{-6}{\sqrt{x}+3}\)
b: ta có \(C=\frac{-6}{\sqrt{x}+3}\) mà \(C=\frac{1}{2}\)
\(\frac{-6}{\sqrt{x}+3}=\frac{1}{2}\)
\(-12=\sqrt{x}+3\)
\(\sqrt{x}=-15\)(Loại)
=> x không có giá trị nào để C=\(\frac{1}{2}\)
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Rút gọn \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}+3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
Rút gọn
P=\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}+3}-\frac{3x-3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
1, rút gọn
\(\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
2, tìm x để P < \(-\frac{1}{2}\)
1)P=\(\left(\frac{2\sqrt{x}\cdot\left(\sqrt{x}-3\right)}{\sqrt{x}+3}+\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}-3}\right):\left(\frac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\right)\)
\(=\frac{-3}{\sqrt{x}+1}\)
2) P <\(\frac{-1}{2}\)\(\Rightarrow-\frac{3}{\sqrt{x}+1}< -\frac{1}{2}\)\(\Leftrightarrow\sqrt{x}< 5\)\(\Leftrightarrow x< 25\)
vậy: khi \(0\le x< 25\)và \(x\ne9\)thì P<\(\frac{-1}{2}\)
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Bài 1:Rút gọna,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)timesleft(1-frac{a-sqrt{a}}{sqrt{a}-1}right)+aleft(ane1;age0right)Bài 2: Rút gọn biểu thứcPfrac{2sqrt{x}-9}{left(sqrt{x}-2right)left(sqrt{x}-3right)}-frac{sqrt{x}+3}{sqrt{x}-2}-frac{2sqrt{x}+1}{3-sqrt{x}}
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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
\(P=\frac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
Bài 1:
a) \(\frac{2}{\sqrt{3}-1}-\frac{2}{\sqrt{3}+1}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}-\frac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}\)
\(=\frac{2\left(\sqrt{3}+1\right)}{2}-\frac{2\left(\sqrt{3}-1\right)}{2}\)
\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)=2\)
b) \(\frac{2}{5-\sqrt{3}}+\frac{3}{\sqrt{6}+\sqrt{3}}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{\left(5-\sqrt{3}\right)\left(5+\sqrt{3}\right)}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{\left(\sqrt{6}+\sqrt{3}\right)\left(\sqrt{6}-\sqrt{3}\right)}\)
\(=\frac{2\left(5+\sqrt{3}\right)}{2}+\frac{3\left(\sqrt{6}-\sqrt{3}\right)}{3}\)
\(=5+\sqrt{3}+\sqrt{6}-\sqrt{3}=5+\sqrt{6}\)
c) ĐK: \(a\ge0;a\ne1\)
\(\left(1+\frac{a+\sqrt{a}}{1+\sqrt{a}}\right).\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{1+\sqrt{a}}\right).\left(1-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)+a\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)+a\)
\(=1-a+a=1\)
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\(B=\frac{3x+\sqrt{9x}-3}{x+\sqrt{x}+2}-\frac{\sqrt{x}-2}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+2}\left(x\ge0,x\ne1\right)\)
Rút Gọn
Rút gọn \(D=\left(\frac{2\sqrt{x}}{\sqrt{x}-3}+\frac{\sqrt{x}}{\sqrt{x}+3}+\frac{3x-3}{9-x}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(\frac{2\sqrt{x}.\left(\sqrt{x}+3\right)+\sqrt{x}.\left(\sqrt{x}-3\right)+3-3x}{\left(\sqrt{x}-3\right).\left(\sqrt{x}+3\right)}:\frac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\)
\(\frac{3.\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+3\right).\left(\sqrt{x}-3\right)}.\frac{\sqrt{x}-3}{\sqrt{x}+1}=\frac{3}{\sqrt{x}+3}\)
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Mình rút gọn như thế này đúng không nhỉ?Pleft(2-frac{sqrt{x}-1}{2sqrt{x}-3}right):left(frac{6sqrt{x}+1}{2x-sqrt{x}-3}+frac{sqrt{x}}{sqrt{x}+1}right)Pleft[frac{2left(2sqrt{x}-3right)}{2sqrt{x}-3}-frac{sqrt{x}-1}{2sqrt{x}-3}right]:left[frac{6sqrt{x}+1}{left(sqrt{x}+1right)left(2sqrt{x}-3right)}+frac{sqrt{x}left(2sqrt{x}-3right)}{left(sqrt{x}+1right)left(2sqrt{x}-3right)}right]Pleft(frac{4sqrt{x}-6}{2sqrt{x}-3}-frac{sqrt{x}-1}{2sqrt{x}-3}right):left(frac{6sqrt{x}+1}{left(sqrt{x}+1right)left(2sqrt{x...
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Mình rút gọn như thế này đúng không nhỉ?
\(P=\left(2-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1}{2x-\sqrt{x}-3}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\)
\(P=\left[\frac{2\left(2\sqrt{x}-3\right)}{2\sqrt{x}-3}-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right]:\left[\frac{6\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}+\frac{\sqrt{x}\left(2\sqrt{x}-3\right)}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right]\)
\(P=\left(\frac{4\sqrt{x}-6}{2\sqrt{x}-3}-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}+\frac{2x-3\sqrt{x}}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right)\)
\(P=\left(\frac{4\sqrt{x}-6-\sqrt{x}+1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1+2x-3\sqrt{x}}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right)\)
\(P=\frac{3\sqrt{x}-5}{2\sqrt{x}-3}:\frac{2x+3\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\)
\(P=\frac{3\sqrt{x}-5}{2\sqrt{x}-3}.\frac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}{2x+3\sqrt{x}+1}\)
\(P=\left(3\sqrt{x}-5\right).\frac{\left(\sqrt{x}+1\right)}{2x+3\sqrt{x}+1}\)
\(P=\frac{3x+3\sqrt{x}-5\sqrt{x}-5}{2x+3\sqrt{x}+1}\)
\(P=\frac{3x-5\sqrt{x}-5}{2x+1}\)
từ dòng cuối là sai rồi bạn à
Bạn bỏ dòng cuối đi còn lại đúng rồi
Ở tử đặt nhân tử chung căn x chung rồi lại đặt căn x +1 chung
Ở mẫu tách 3 căn x ra 2 căn x +căn x rồi đặt nhân tử 2 căn x ra
rút gọn được \(\frac{3\sqrt{x}-5}{2\sqrt{x}+1}\)
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