rút gọn A=\(\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{x^2-4x-1}{x^2-1}\right)\times\frac{x+2003}{x}\)
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Rút gọn \(B=\left(x^4-x+\frac{x-3}{x^3+1}\times\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right)\times\frac{4x^2+6x+1}{\left(x+3\right)\left(4-x\right)}\)
A=\(\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{\left(x-1\right)^2}{x^2-1}\right).\frac{x+2003}{x}.\)
a) ĐK? Rút gọn A?
Giusp mik với mik đang cần gấp ! thanks nhìu ạ !
\(A=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{\left(x-1\right)^2}{x^2-1}\right).\frac{x+2003}{x}\)ĐKXĐ: \(x\ne-1;0;1\)
\(A=\frac{\left(x+1\right)^2-\left(x-1\right)^2+\left(x-1\right)^2}{\left(x+1\right)\left(x-1\right)}.\frac{x+2003}{x}\)
\(A=\frac{\left(x+1\right)^2}{\left(x+1\right)\left(x-1\right)}.\frac{x+2003}{x}\)
\(A=\frac{x+1}{x-1}.\frac{x+2003}{x}\)
\(A=\frac{x^2+2004x+2003}{x^2-x}\)
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Cho \(B=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{x^2-4x-1}{1-x^2}\right)\times\frac{x-2014}{x+1}\)
a) Rút gọn B
b) Với giá trị nguyên nào của x thì A có giá trị nguyên
a) ĐKXĐ : \(x\ne\pm1\)
+ \(B=\left(\frac{\left(x+1\right)^2-\left(x-1\right)^2+\left(x^2-4x-1\right)}{x^2-1}\right)\cdot\frac{x-2014}{x-1}\)
\(B=\frac{4x+x^2-4x-1}{x^2-1}\cdot\frac{x-2014}{x+1}\)
\(B=\frac{x^2-1}{x^2-1}\cdot\frac{x-2014}{x+1}=\frac{x-2014}{x+1}\)\
b) B có giá trị nguyên
\(\Leftrightarrow x-2014⋮x+1\)
\(\Leftrightarrow x+1-2015⋮x+1\)
\(\Leftrightarrow2015⋮x+1\)
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Rút gọn biểu thức
1)\(\frac{c\left(a+c\right)-a\left(a-c\right)}{\frac{c}{a-c}-\frac{a}{a+ c}}\)
2) \(\frac{\frac{x^2-y^2}{x}}{\frac{1}{x}-\frac{1}{y}}\)
3) \(x:\frac{x-1}{2}-\frac{\left(x-1\right)\left(x^2+4x+1\right)}{2x^2+2x}.\frac{-4x}{\left(x-1\right)^2}-\frac{4x^2}{x^2-1}\)
Rút gọn biểu thức sau: A=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+4\right)\left(3-x\right)}\)
\(K=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{x^2-4x-1}{x^2-1}\right).\frac{x+2003}{x}\)
a) Tìm điều kiện của x để K xác định.
b) Rút gọn K
c) Tìm x thuộc Z để K có giá trị nguyên.
a)ĐKXĐ:
\(x-1\ne0;x+1\ne0;x\ne0\)
\(\Leftrightarrow x\ne1;x\ne-1;x\ne0\)
b)\(K=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{x^2-4x-1}{x^2-1}\right).\frac{x+2003}{x}\)
\(=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{x^2-4x-1}{\left(x-1\right)\left(x+1\right)}\right).\frac{x+2003}{x}\)
\(=\left(\frac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}+\frac{x^2-4x-1}{\left(x-1\right)\left(x+1\right)}\right).\frac{x+2003}{x}\)
\(=\frac{x^2+2x+1+x^2-2x+1+x^2-4x-1}{\left(x-1\right)\left(x+1\right)}.\frac{x+2003}{x}\)
\(=\frac{3x^2-4x+1}{\left(x-1\right)\left(x+1\right)}.\frac{x+2003}{x}\)
\(=\frac{3x^2-3x-x+1}{\left(x-1\right)\left(x+1\right)}.\frac{x+2003}{x}\)
\(=\frac{3x.\left(x-1\right)-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}.\frac{x+2003}{x}\)
\(=\frac{\left(x-1\right)\left(3x-1\right)}{\left(x-1\right)\left(x+1\right)}.\frac{x+2003}{x}\)
\(=\frac{\left(3x-1\right)\left(x+2003\right)}{\left(x+1\right).x}\)
\(=\frac{3x^2+6008x-2003}{x^2+x}\)
câu c bí
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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\(\left(\frac{\sqrt{x}+1}{x-1}-\frac{\sqrt{x}+2}{\left(\sqrt{x}+1\right)^2}\right)\times\frac{1-x^2}{2}\)
Cho \(K=\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}+\frac{x^2-4x-1}{x^2-1}\right).\frac{x+2003}{x}\)
a)Tìm điều kiện của x để K xác định.
b)Rút gọn K
c)Tìm x thuộc Z để K có giá trị nguyên.