p = (1/(sqrt(x)) - 2/(1 + sqrt(x))) - (x + sqrt(x))/(1 - sqrt(x))
Những câu hỏi liên quan
LARGE 7)Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2sqrt{x}+2}{x-1}Gfrac{sqrt{x}+1}{sqrt{x}-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2}{sqrt{x}-1}Gfrac{(sqrt{x}+1)^2+(sqrt{x}-1)^2-2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2x-2sqrt{x}}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}(sqrt{x}-1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}}{sqrt{x}+1}8)H(frac{1}{sqrt{x}-1}+frac{sqrt{x}}{x-1}):(frac{sqrt{x}}{sqrt{x}-1}-...
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\[\LARGE 7)G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2\sqrt{x}+2}{x-1}\\G=\frac{\sqrt{x}+1}{\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2}{\sqrt{x}-1}\\G=\frac{(\sqrt{x}+1)^2+(\sqrt{x}-1)^2-2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2x-2\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}}{\sqrt{x}+1}\\8)H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}):(\frac{\sqrt{x}}{\sqrt{x}-1}-1)\\H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}):(\frac{\sqrt{x}-(\sqrt{x}-1)}{\sqrt{x}-1})\\H=\frac{\sqrt{x}+1+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}.(\sqrt{x}-1)\\H=\frac{2\sqrt{x}}{\sqrt{x}+1}\]
frac{x+1}{2left(x-1right)}+frac{2}{2left(sqrt{x}+1right)}+frac{sqrt{x}}{sqrt{x}left(sqrt{x}-1right)}.frac{left(x+1right).sqrt{x}}{2sqrt{x}left(sqrt{x}-1right)left(sqrt{x}+1right)}+frac{2sqrt{x}left(sqrt{x}-1right)}{2sqrt{x}left(sqrt{x}-1right)left(sqrt{x}+1right)}+frac{2sqrt{x}left(sqrt{x}+1right)}{2sqrt{x}left(sqrt{x}-1right)left(sqrt{x}+1right)}.frac{xsqrt{x}+sqrt{x}}{2sqrt{x}left(sqrt{x}-1right)left(sqrt{x}+1right)}+frac{2x-2sqrt{x}}{2sqrt{x}left(sqrt{x}-1right)left(sqrt{x}+1right)}+frac{2x+2...
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\(=\frac{x+1}{2\left(x-1\right)}+\frac{2}{2\left(\sqrt{x}+1\right)}+\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}.\)
=\(\frac{\left(x+1\right).\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{2\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{2\sqrt{x}\left(\sqrt{x}+1\right)}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\)
=\(\frac{x\sqrt{x}+\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{2x-2\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{2x+2\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\)
=\(\frac{x\sqrt{x}+4x+\sqrt{x}}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
=\(\frac{\sqrt{x}\left(x+4\sqrt{x}+1\right)}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
=\(\frac{\sqrt{x}\left(\sqrt{x}+1\right)^2}{2\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
=\(\frac{\sqrt{x}+1}{2\left(\sqrt{x}-1\right)}\)
LƯU Ý: CAP NÀY CHỈ LÀ CAP NHÁP
Bleft(frac{xsqrt{x}+x+sqrt{x}}{xsqrt{x}-1}-frac{sqrt{x}+3}{1-sqrt{x}}right).frac{x-1}{2x+sqrt{x}-1} ĐKXĐ: ...frac{left(xsqrt{x}+x+sqrt{x}right)left(1-sqrt{x}right)-left(sqrt{x}+3right)left(xsqrt{x}-1right)}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2x+2sqrt{x}-sqrt{x}-1}frac{xsqrt{x}+x+sqrt{x}-x^2-xsqrt{x}-x-x^2+sqrt{x}-3xsqrt{x}+3}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2sqrt{x}left(sqrt{x}+1right)-left(sqrt{x}+1right)}frac{-3xsqrt{x}+2sqrt{x}-2x^2+3}{left(xsqrt{x}-1ri...
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\(B=\left(\frac{x\sqrt{x}+x+\sqrt{x}}{x\sqrt{x}-1}-\frac{\sqrt{x}+3}{1-\sqrt{x}}\right).\frac{x-1}{2x+\sqrt{x}-1}\) ĐKXĐ: ...
\(=\frac{\left(x\sqrt{x}+x+\sqrt{x}\right)\left(1-\sqrt{x}\right)-\left(\sqrt{x}+3\right)\left(x\sqrt{x}-1\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2x+2\sqrt{x}-\sqrt{x}-1}\)
\(=\frac{x\sqrt{x}+x+\sqrt{x}-x^2-x\sqrt{x}-x-x^2+\sqrt{x}-3x\sqrt{x}+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2\sqrt{x}\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)}\)
\(=\frac{-3x\sqrt{x}+2\sqrt{x}-2x^2+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3-3x\sqrt{x}+2\sqrt{x}-2x^2}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3\left(1-x\sqrt{x}\right)+2\sqrt{x}\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(2\sqrt{x}+3\right)\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2\sqrt{x}-1}\)
\(=\frac{2\sqrt{x}+3}{2\sqrt{x}-1}\)
left(dfrac{x+2}{xsqrt{x}-1}+dfrac{sqrt{x}}{x+sqrt{x}+1}+dfrac{1}{1-sqrt{x}}right):dfrac{sqrt{x}-1}{2}
left(dfrac{x+2}{left(sqrt{x}-1right)left(x+sqrt{x}+1right)}+dfrac{sqrt{x}left(sqrt{x}-1right)}{left(sqrt{x}-1right)left(x+sqrt{x}+1right)}-dfrac{1}{sqrt{x}-1}right).dfrac{2}{sqrt{x}-1}
dfrac{x+2+x-sqrt{x}-x-sqrt{x}-1}{left(sqrt{x}-1right)left(x+sqrt{x}+1right)}.dfrac{2}{sqrt{x}-1}dfrac{sqrt{x}-1}{x+sqrt{x}+1}.dfrac{2}{sqrt{x}-1}dfrac{2}{x+sqrt{x}+1}
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\(\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{2}\)
\(=\left(\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}-\dfrac{1}{\sqrt{x}-1}\right).\dfrac{2}{\sqrt{x}-1}\)
= \(\dfrac{x+2+x-\sqrt{x}-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\dfrac{2}{\sqrt{x}-1}\)=\(\dfrac{\sqrt{x}-1}{x+\sqrt{x}+1}.\dfrac{2}{\sqrt{x}-1}=\dfrac{2}{x+\sqrt{x}+1}\)
Rút gọn biểu thức frac{left(sqrt{x-4sqrt{x-4}}+sqrt{x+4sqrt{x-4}}right)left(sqrt{x-1}-1right)}{sqrt{x-2sqrt{x-1}}}b,sqrt{x-2sqrt{x-1}+sqrt{x+2sqrt{x-1}}}1le xle2c, sqrt{x+6sqrt{x-9}}+sqrt{x-6sqrt{x-9}}x18d, frac{1}{2left(1+sqrt{x+2}right)}+frac{1}{2left(1-2sqrt{x+2}right)}e,frac{1}{sqrt{x+2sqrt{x-1}}}-frac{1}{sqrt{x-2sqrt{x-1}}}
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Rút gọn biểu thức
\(\frac{\left(\sqrt{x-4\sqrt{x-4}}+\sqrt{x+4\sqrt{x-4}}\right)\left(\sqrt{x-1}-1\right)}{\sqrt{x-2\sqrt{x-1}}}\)
b,\(\sqrt{x-2\sqrt{x-1}+\sqrt{x+2\sqrt{x-1}}}1\le x\le2\)
c, \(\sqrt{x+6\sqrt{x-9}}+\sqrt{x-6\sqrt{x-9}}x>18\)
d, \(\frac{1}{2\left(1+\sqrt{x+2}\right)}+\frac{1}{2\left(1-2\sqrt{x+2}\right)}\)
e,\(\frac{1}{\sqrt{x+2\sqrt{x-1}}}-\frac{1}{\sqrt{x-2\sqrt{x-1}}}\)
Rút gọn
A=\(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\)
B=\(\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}+4\sqrt{x}\right).\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)\)
C=\(\left(\frac{1}{\sqrt{x}+1}-\frac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right):\left(\frac{1}{\sqrt{x}-1}-\frac{2}{x-1}\right)\)
Pleft(frac{sqrt{x}+2}{sqrt{x}+1}-frac{x-sqrt{x}-3}{x-sqrt{x}-2}right):left(frac{x-sqrt{x}}{x-sqrt{x}-2}+frac{2}{sqrt{x}-2}right)frac{left(sqrt{x}+2right)left(sqrt{x}-2right)-x+sqrt{x}+3}{left(sqrt{x}+1right)left(sqrt{x}-2right)}:frac{x-sqrt{x}+2left(sqrt{x}+1right)}{left(sqrt{x}+1right)left(sqrt{x}-2right)}frac{x-4-x+3+sqrt{x}}{left(sqrt{x}+1right)left(sqrt{x}-2right)}.frac{left(sqrt{x}+1right)left(sqrt{x}-2right)}{x-sqrt{x}+2sqrt{x}+2}frac{sqrt{x}-1}{x+sqrt{x}+2}
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\(P=\left(\frac{\sqrt{x}+2}{\sqrt{x}+1}-\frac{x-\sqrt{x}-3}{x-\sqrt{x}-2}\right):\left(\frac{x-\sqrt{x}}{x-\sqrt{x}-2}+\frac{2}{\sqrt{x}-2}\right)\)
\(=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-x+\sqrt{x}+3}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}:\frac{x-\sqrt{x}+2\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}\)
\(=\frac{x-4-x+3+\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}.\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{x-\sqrt{x}+2\sqrt{x}+2}\)
\(=\frac{\sqrt{x}-1}{x+\sqrt{x}+2}\)
#)Hỏi j đi bn, bn ph hỏi cái j chứ làm lun rùi còn để cộng đồng ngắm ak ???
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Bó cả tay lẫn chân !!! Bất lực như gặp cực hình !
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Chắc là bạn ấy hỏi bạn ấy làm có đúng ko ha gì đó ?
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Xem thêm câu trả lời
rút gọn:a)left(frac{1}{2+2sqrt{x}}+frac{1}{2-2sqrt{x}}-frac{x^2+1}{1-x^2}right)timesleft(1+frac{1}{x}right)b)left(frac{2sqrt{xy}}{x-y}+frac{sqrt{x}-sqrt{y}}{2sqrt{x}+sqrt{y}}right)timesfrac{2sqrt{x}}{sqrt{x}+sqrt{y}}+frac{sqrt{y}}{sqrt{y}-sqrt{x}}c)left(frac{x-1}{sqrt{x}-1}+frac{xsqrt{x}-1}{1-x}right)divfrac{left(sqrt{x}-1right)^2+sqrt{x}}{sqrt{x}+1}
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rút gọn:
a)\(\left(\frac{1}{2+2\sqrt{x}}+\frac{1}{2-2\sqrt{x}}-\frac{x^2+1}{1-x^2}\right)\times\left(1+\frac{1}{x}\right)\)
b)\(\left(\frac{2\sqrt{xy}}{x-y}+\frac{\sqrt{x}-\sqrt{y}}{2\sqrt{x}+\sqrt{y}}\right)\times\frac{2\sqrt{x}}{\sqrt{x}+\sqrt{y}}+\frac{\sqrt{y}}{\sqrt{y}-\sqrt{x}}\)
c)\(\left(\frac{x-1}{\sqrt{x}-1}+\frac{x\sqrt{x}-1}{1-x}\right)\div\frac{\left(\sqrt{x}-1\right)^2+\sqrt{x}}{\sqrt{x}+1}\)
a, dk \(x\ge0.x\ne1\)
\(\left(\frac{1+\sqrt{x}+1-\sqrt{x}}{2\left(1-x\right)}-\frac{x^2+1}{1-x^2}\right)\left(\frac{x+1}{x}\right)\)=\(\left(\frac{1}{1-x}-\frac{x^2+1}{1-x^2}\right)\left(\frac{x+1}{x}\right)\)
=\(\left(\frac{1+x-x^2-1}{1-x^2}\right)\left(\frac{x+1}{x}\right)=\frac{x\left(1-x\right)\left(x+1\right)}{x\left(1-x\right)\left(1+x\right)}=1\)
phan b,c ban tu lam not nhe dai lam mk ko lam dau mk co vc ban rui
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rút gọn
dfrac{9-x}{sqrt{x}+3}-dfrac{9-6sqrt{x}+x}{sqrt{x}-3}-6 (với x_9)
left(dfrac{2sqrt{x}}{xsqrt{x}+x+sqrt{x}+1}-dfrac{1}{sqrt{x}+1}right)/left(dfrac{2sqrt{x}}{sqrt{x}+1}-1right) (với x0, x#1)
sqrt{x+12+6sqrt{x+3}}-sqrt{x+12-6sqrt{x+3}} ( với x_6)
sqrt{m^2+6m+9}+sqrt{m^2-6m+9} (m bát kì)
dfrac{xsqrt{x}-1}{x-sqrt{x}}-dfrac{xsqrt{x}+1}{x+sqrt{x}}dfrac{x+1}{sqrt{x}}
dfrac{xsqrt{y}+ysqrt{x}}{sqrt{xy}}/dfrac{sqrt{x}-sqrt{y}}{x-y}
left(dfrac{1}{sqrt{x}-1}+dfrac{1}{sqrt{x}+1}right)left...
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rút gọn
\(\dfrac{9-x}{\sqrt{x}+3}-\dfrac{9-6\sqrt{x}+x}{\sqrt{x}-3}-6\) (với x>_9)
\(\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right)/\left(\dfrac{2\sqrt{x}}{\sqrt{x}+1}-1\right)\) (với x>=0, x#1)
\(\sqrt{x+12+6\sqrt{x+3}}-\sqrt{x+12-6\sqrt{x+3}}\) ( với x>_6)
\(\sqrt{m^2+6m+9}+\sqrt{m^2-6m+9}\) (m bát kì)
\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\dfrac{x+1}{\sqrt{x}}\)
\(\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}/\dfrac{\sqrt{x}-\sqrt{y}}{x-y}\)
\(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(\left(\dfrac{\sqrt{x}+2}{3\sqrt{x}}+\dfrac{2}{\sqrt{x}+1}-3\right)/\dfrac{2-4\sqrt{x}}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1-x}{3\sqrt{x}}\)
a: \(A=\dfrac{-\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\sqrt{x}+3}-\dfrac{\left(\sqrt{x}-3\right)^2}{\sqrt{x}-3}-6\)
\(=-\sqrt{x}+3-\sqrt{x}+3-6=-2\sqrt{x}\)
b: \(\left(\dfrac{2\sqrt{x}}{x\sqrt{x}+x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}+1}\right):\left(\dfrac{2\sqrt{x}}{\sqrt{x}+1}-1\right)\)
\(=\left(\dfrac{2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(x+1\right)}-\dfrac{1}{\sqrt{x}+1}\right):\dfrac{2\sqrt{x}-\sqrt{x}-1}{\sqrt{x}+1}\)
\(=\dfrac{2\sqrt{x}-x-1}{\left(\sqrt{x}+1\right)\left(x+1\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{1}{x+1}\)
g: \(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+1}\right)\left(\dfrac{x-1}{\sqrt{x}+1}-2\right)\)
\(=\dfrac{\sqrt{x}+1+\sqrt{x}-1}{x-1}\cdot\left(\sqrt{x}-1-2\right)\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-3\right)}{x-1}\)
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23 tháng 8 2021 lúc 19:43
Rút gọn:1) Pdfrac{x^2-sqrt{x}}{x+sqrt{x}+1}-dfrac{2x+sqrt{x}}{sqrt{x}}+dfrac{2left(x-1right)}{sqrt{x}-1}2)Aleft(dfrac{2sqrt{x}+x}{xsqrt{x}-1}-dfrac{1}{sqrt{x}-1}right):left(1-dfrac{sqrt{x}+2}{x+sqrt{x}+1}right)3) Aleft(dfrac{1}{sqrt{a}-1}-dfrac{1}{sqrt{a}}right):left(dfrac{sqrt{a}+1}{sqrt{a}-2}-dfrac{sqrt{a}+2}{sqrt{a}-1}right) 4) Aleft(dfrac{1}{sqrt{x}+1}-dfrac{2sqrt{x}-2}{xsqrt{x}-sqrt{x}+x-1}right):left(dfrac{1}{sqrt{x}-1}-dfrac{2}{x-1}right)Mng giúp e vs ạ, cần gấp :
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Rút gọn:
1) \(P=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
2)\(A=\left(\dfrac{2\sqrt{x}+x}{x\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
3) \(A=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
4) \(A=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right):\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2}{x-1}\right)\)
Mng giúp e vs ạ, cần gấp :<
1: Ta có: \(P=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=x-\sqrt{x}-2\sqrt{x}-1+2\sqrt{x}+2\)
\(=x-\sqrt{x}+1\)
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2: Ta có: \(A=\left(\dfrac{x+2\sqrt{x}}{x\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
\(=\dfrac{x+2\sqrt{x}-x+\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}:\dfrac{x+\sqrt{x}+1-\sqrt{x}-2}{\left(x+\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\dfrac{x+\sqrt{x}+1}{x-1}\)
\(=\dfrac{1}{x-1}\)
3: Ta có: \(A=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(=\dfrac{\sqrt{a}-\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-a+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)
\(=\dfrac{\sqrt{a}-2}{3\sqrt{a}}\)
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