Em coi lại đề bài, \(8\left(x+\dfrac{1}{x}\right)\) hay \(8\left(x+\dfrac{1}{x}\right)^2\) nhỉ?
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giải phương trình
1)\(\left(x-2\right)\left(3+2x\right)-2x\left(x+5\right)=6\)
2)\(x^2-4-\left(x-5\right)\left(x-2\right)=0\)
3)\(\dfrac{x-3}{3}-\dfrac{x+2}{2}=\dfrac{x}{6}\)
4)\(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}+\dfrac{3x-1}{x-4}-6\)
5)\(\dfrac{96}{x^2-16}=\dfrac{2x-1}{x+4}+\dfrac{3x-1}{x-4}-6\)
Bt thực hiện phép tính:
a/dfrac{1}{xleft(x+1right)}+dfrac{1}{left(x+1right)left(x+2right)}+dfrac{1}{left(x+2right)left(x+3right)}+...+dfrac{1}{left(x+2017right)left(x+2018right)}
b/dfrac{1}{xleft(x+2right)left(x+4right)}+dfrac{1}{left(x+2right)left(x+4right)left(x+6right)}+...+dfrac{1}{left(x+96right)left(x+98right)left(x+100right)}
GIÚP MÌNH VỚI!!!!!! THỨ HAI THẦY KIỂM TRA RỒI!
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Bt thực hiện phép tính:
a/\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+...+\dfrac{1}{\left(x+2017\right)\left(x+2018\right)}\)
b/\(\dfrac{1}{x\left(x+2\right)\left(x+4\right)}+\dfrac{1}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}+...+\dfrac{1}{\left(x+96\right)\left(x+98\right)\left(x+100\right)}\)
GIÚP MÌNH VỚI!!!!!! THỨ HAI THẦY KIỂM TRA RỒI!
Chứng minh đẳng thức :
a) left(dfrac{x^2-2x}{2x^2+8}-dfrac{2x^2}{8-4x+2x^2-x^3}right)left(1-dfrac{1}{x}-dfrac{2}{x^2}right)dfrac{x+1}{2x}
b) left[dfrac{2}{3x}-dfrac{2}{x+1}left(dfrac{x+1}{3}-x-1right)right]:dfrac{x-1}{x}dfrac{2x}{x-1}
c) left[dfrac{2}{left(x+1right)^3}.left(dfrac{1}{x}+1right)+dfrac{1}{x^2+2x+1}left(dfrac{1}{x^2}+1right)right]:dfrac{x-1}{x^3}dfrac{x}{x-1}
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Chứng minh đẳng thức :
a) \(\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)=\dfrac{x+1}{2x}\)
b) \(\left[\dfrac{2}{3x}-\dfrac{2}{x+1}\left(\dfrac{x+1}{3}-x-1\right)\right]:\dfrac{x-1}{x}=\dfrac{2x}{x-1}\)
c) \(\left[\dfrac{2}{\left(x+1\right)^3}.\left(\dfrac{1}{x}+1\right)+\dfrac{1}{x^2+2x+1}\left(\dfrac{1}{x^2}+1\right)\right]:\dfrac{x-1}{x^3}=\dfrac{x}{x-1}\)
Giải các phương trình
a)\(\dfrac{15}{4}-2,5:\left|\dfrac{3}{4}x+\dfrac{1}{2}\right|=3\)
b) \(6,5-\dfrac{9}{4}:\left|x+\dfrac{1}{3}\right|=2\)
c) \(\left|\dfrac{5}{4}x-\dfrac{7}{2}\right|-\left|\dfrac{5}{8}x+\dfrac{3}{5}\right|=0\)
Thực hiện các phép tính :
a) left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)
b) left(dfrac{2}{x-2}-dfrac{2}{x+2}right).dfrac{x^2+4x+4}{8}
c) left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}
d) left(dfrac{x}{x^2-25}-dfrac{x-5}{x^2+5x}right):dfrac{2x-5}{x^2+5x}+dfrac{x}{5-x}
e) left(dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+dfrac{y}{x^2+y^2}right):left(dfrac{1}{x-y}-dfrac{2xy}{x^3-x^2y+xy^2-y^3}right)
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Thực hiện các phép tính :
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)
c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Thực hiên phép tính:
a) dfrac{1}{left(a-bright)left(b-cright)}+dfrac{1}{left(b-cright)left(c-aright)}+dfrac{1}{left(c-aright)left(a-bright)}
b) dfrac{left[a^2-left(b+cright)^2right]left(a+b-cright)}{left(a+b+cright)left(a^2+c^2-2ac-b^2right)}
c) dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+dfrac{3}{x^3-2x^2+x}
d) left[dfrac{x^2-y^2}{xy}-dfrac{1}{x+y}left(dfrac{x^2}{y}-dfrac{y^2}{x}right)right]:dfrac{x-y}{x}
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Thực hiên phép tính:
a) \(\dfrac{1}{\left(a-b\right)\left(b-c\right)}+\dfrac{1}{\left(b-c\right)\left(c-a\right)}+\dfrac{1}{\left(c-a\right)\left(a-b\right)}\)
b) \(\dfrac{\left[a^2-\left(b+c\right)^2\right]\left(a+b-c\right)}{\left(a+b+c\right)\left(a^2+c^2-2ac-b^2\right)}\)
c) \(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
d) \(\left[\dfrac{x^2-y^2}{xy}-\dfrac{1}{x+y}\left(\dfrac{x^2}{y}-\dfrac{y^2}{x}\right)\right]:\dfrac{x-y}{x}\)
rút gọn các phân thức
a,\(\dfrac{7xy^3\left(x-2y\right)}{14x^2y^2\left(x-2y\right)^2}\)
b,\(\dfrac{4a^2-8ab}{2\left(2b-a\right)^3}\)
c,\(\dfrac{3x^3-3x}{x^4-1}\)
d,\(\dfrac{45x\left(3-x\right)}{15x\left(x-3\right)^3}\)
Bài 1: Rút gon
a) B=\(\left(\dfrac{x}{3x-9}+\dfrac{2x-3}{3x-x^2}\right).\dfrac{3x^2-9x}{x^2+6x+9}\)
b) A=\(\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)
cho A= \(\dfrac{x.\left(1-x^2\right)^2}{1+x^2}:\left[\left(\dfrac{1-x^3}{1-x}+x\right).\left(\dfrac{1+x^3}{1+x}-x\right)\right]\)
a) rút gọn
b.tìm A khi x = \(\dfrac{-1}{2}\)
c) tìm x để 2A =1