Bài 3 ( 3đ) : Thực hiện phép tính
\(\dfrac{y}{x-y}-\dfrac{x^3-xy^2}{x^2+y^2}.\left(\dfrac{x}{x^2-2xy+y^2}-\dfrac{y}{x^2-y^2}\right)\)
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Thực hiện phép tính , rút gọn bt
\(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
\(\dfrac{x+y}{2\left(x-y\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
Thực hiện phép tính sau:
d) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^2-x^2y+xy^2-y^3}\right)\)
\(=\left(\dfrac{x\left(x+y\right)}{x^2\left(x+y\right)+y^2\left(x+y\right)}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^2\left(x-y\right)+y^2\left(x-y\right)}\right)\)
\(=\dfrac{x+y}{x^2+y^2}:\left(\dfrac{1}{x-y}-\dfrac{2xy}{\left(x-y\right)\left(x^2+y^2\right)}\right)\)
\(=\dfrac{x+y}{x^2+y^2}:\dfrac{x^2+y^2-2xy}{\left(x-y\right)\left(x^2+y^2\right)}\)
\(=\dfrac{x+y}{x^2+y^2}\cdot\dfrac{\left(x-y\right)\left(x^2+y^2\right)}{\left(x-y\right)^2}\)
\(=\dfrac{x+y}{x-y}\)
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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)
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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 hiện phép tính:
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^3+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
c) \(\left(\dfrac{x-y}{x+y}+\dfrac{x+y}{x-y}\right).\left(\dfrac{x^2+y^2}{2xy}+1\right).\dfrac{xy}{x^2+y^2}\)
a: \(=\left(\dfrac{9}{x\left(x-3\right)\left(x+3\right)}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x\left(x+3\right)}-\dfrac{x}{3\left(x+3\right)}\right)\)
\(=\dfrac{9+x^2-3x}{x\left(x-3\right)\left(x+3\right)}:\dfrac{3\left(x-3\right)-x^2}{3x\left(x+3\right)}\)
\(=\dfrac{x^2-3x+9}{x\left(x-3\right)\left(x+3\right)}\cdot\dfrac{3x\left(x+3\right)}{3x-9-x^2}\)
\(=\dfrac{3}{x-3}\cdot\dfrac{-\left(x^2-3x+9\right)}{x^2-3x+9}=\dfrac{-3}{x-3}\)
b: \(=\dfrac{x+1}{x+2}:\left(\dfrac{\left(x+2\right)\left(x+1\right)}{\left(x+3\right)^2}\right)\)
\(=\dfrac{x+1}{x+2}\cdot\dfrac{\left(x+3\right)^2}{\left(x+2\right)\left(x+1\right)}=\dfrac{\left(x+3\right)^2}{\left(x+2\right)^2}\)
c: \(=\dfrac{x^2-2xy+y^2+x^2+2xy+y^2}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{x^2+2xy+y^2}{2xy}\cdot\dfrac{xy}{x^2+y^2}\)
\(=\dfrac{2\left(x^2+y^2\right)}{\left(x-y\right)\left(x+y\right)}\cdot\dfrac{\left(x+y\right)^2}{x^2+y^2}\cdot\dfrac{1}{2}\)
\(=\dfrac{\left(x+y\right)}{x-y}\)
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Thực hiện phép tính:a) dfrac{x+2y}{xy}divdfrac{x^2+4xy+4y^2}{2x^2}b) dfrac{4x^3-xy^2}{x^2+xy+y^2}divdfrac{left(2x-yright)^3}{x^3-y^3}c) dfrac{x+3}{x+2}divdfrac{3x+9}{2x-1}divdfrac{4x-2}{2x+4}d) dfrac{x+1}{x+2}divleft(dfrac{2x^2}{2x-3}timesdfrac{3x+3}{4x^3}right)
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Thực hiện phép tính:
a) \(\dfrac{x+2y}{xy}\div\dfrac{x^2+4xy+4y^2}{2x^2}\)
b) \(\dfrac{4x^3-xy^2}{x^2+xy+y^2}\div\dfrac{\left(2x-y\right)^3}{x^3-y^3}\)
c) \(\dfrac{x+3}{x+2}\div\dfrac{3x+9}{2x-1}\div\dfrac{4x-2}{2x+4}\)
d) \(\dfrac{x+1}{x+2}\div\left(\dfrac{2x^2}{2x-3}\times\dfrac{3x+3}{4x^3}\right)\)
a: \(=\dfrac{x+2y}{xy}\cdot\dfrac{2x^2}{\left(x+2y\right)^2}=\dfrac{2x}{y\left(x+2y\right)}\)
b: \(=\dfrac{x\left(4x^2-y^2\right)}{x^2+xy+y^2}\cdot\dfrac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(2x-y\right)^3}\)
\(=\dfrac{x\left(x-y\right)\left(2x+y\right)\left(2x-y\right)}{\left(2x-y\right)^3}\)
\(=\dfrac{x\left(x-y\right)\left(2x+y\right)}{\left(2x-y\right)^2}\)
c: \(=\dfrac{x+3}{x+2}\cdot\dfrac{2x-1}{3\left(x+3\right)}\cdot\dfrac{2\left(x+2\right)}{2\left(2x-1\right)}\)
=1/3
d: \(=\dfrac{x+1}{x+2}:\left(\dfrac{1}{2x}\cdot\dfrac{3x+3}{2x-3}\right)\)
\(=\dfrac{x+1}{x+2}\cdot\dfrac{2x\left(2x-3\right)}{3\left(x+1\right)}=\dfrac{2x\left(2x-3\right)}{3\left(x+2\right)}\)
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thực hiên phép tính
a.\(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
b.\(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
a, \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)=\(\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\) = \(\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\) =\(\dfrac{x+y}{4}\)
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a. \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
\(=\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\)
\(=\dfrac{x+y}{4}\)
b. \(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{\left(x+1\right)\left(x-1\right)}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{2}{x-1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{2\left(x-1\right)}\)
\(=\dfrac{x+1}{2\left(x-1\right)}\)
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a) Ta có: \(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
\(=\dfrac{x^2+2xy+y^2}{4\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2}{4\left(x+y\right)}\)
\(=\dfrac{x+y}{4}\)
b) Ta có: \(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{\left(x-1\right)\left(x+1\right)}\cdot\dfrac{x+1}{2}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{2}{x-1}\)
\(=\dfrac{x+5}{2\left(x-1\right)}-\dfrac{4}{2\left(x-1\right)}\)
\(=\dfrac{x+5-4}{2\left(x-1\right)}\)
\(=\dfrac{x+1}{2x-2}\)
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Thực hiện các phép tính sau:
a).left(dfrac{2x+1}{2x-1}-dfrac{2x-1}{2x+1}right):dfrac{4x}{10x-5}
b). left(dfrac{1}{x^2+1}-dfrac{2-x}{x+1}right):left(dfrac{1}{x}+x-2right)
c). dfrac{1}{x-1}-dfrac{x^3-x}{x^2+1}.left(dfrac{1}{x^2-2x+1}+dfrac{1}{1-x^2}right)
d). 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 sau:
a).\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b). \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c). \(\dfrac{1}{x-1}-\dfrac{x^3-x}{x^2+1}.\left(\dfrac{1}{x^2-2x+1}+\dfrac{1}{1-x^2}\right)\)
d). \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
a) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)\left(2x+1\right)}{2x^2-1}-\dfrac{\left(2x-1\right)\left(2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1\right)^2-\left(2x-1\right)^2}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\left(\dfrac{\left(2x+1-2x-1\right)\left(2x+1+2x-1\right)}{2x^2-1}\right):\dfrac{4x}{10x-5}\)
\(=\dfrac{4x}{2x^2-1}.\dfrac{5\left(2x-1\right)}{4x}\)
\(=\dfrac{5}{2x+1}\)
b) \(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1}{x^2+1}-\dfrac{x\left(2-x\right)}{x\left(x+1\right)}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{1}{x}+\dfrac{x^2}{x}-\dfrac{2x}{x}\right)\)
\(=\left(\dfrac{1-2x+x^2}{x^2+1}\right):\left(\dfrac{x^2-2x+1}{x}\right)\)
\(=\dfrac{\left(x-1\right)^2}{x^2+1}.\dfrac{x}{\left(x-1\right)^2}\)
\(=\dfrac{x}{x^2+1}\)
c) d) Tự làm đi mình làm biếng quass >.< ^^
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23 tháng 12 2022 lúc 16:21
1) Thực hiện các phép tính sau ( giả thiết các phân thức đã cho có nghĩa).a)dfrac{x^3}{x-1}-dfrac{x^2}{x+1}-dfrac{1}{x-1}+dfrac{1}{x+1}b)dfrac{x+y}{2.left(x-yright)}-dfrac{x-y}{2.left(x+yright)}+dfrac{2y^2}{x^2-y^2}c)dfrac{x+5}{2x-4}.dfrac{4-2x}{x+2}d) dfrac{8}{x^2+2x-3}+dfrac{2}{x+3}+dfrac{1}{x-1}Mình đang cần gấp ah
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1) Thực hiện các phép tính sau ( giả thiết các phân thức đã cho có nghĩa).
a)\(\dfrac{x^3}{x-1}\)-\(\dfrac{x^2}{x+1}\)-\(\dfrac{1}{x-1}\)+\(\dfrac{1}{x+1}\)
b)\(\dfrac{x+y}{2.\left(x-y\right)}\)-\(\dfrac{x-y}{2.\left(x+y\right)}\)+\(\dfrac{2y^2}{x^2-y^2}\)
c)\(\dfrac{x+5}{2x-4}\).\(\dfrac{4-2x}{x+2}\)
d) \(\dfrac{8}{x^2+2x-3}\)+\(\dfrac{2}{x+3}\)+\(\dfrac{1}{x-1}\)
Mình đang cần gấp ah
a.
\(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}=\dfrac{x^3-1}{x-1}-\dfrac{x^2-1}{x+1}\)
\(=\dfrac{\left(x-1\right)\left(x^2+x+1\right)}{x-1}-\dfrac{\left(x-1\right)\left(x+1\right)}{x+1}\)
\(=x^2+x+1-\left(x-1\right)=x^2+2\)
b.
\(\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
\(=\dfrac{\left(x+y\right)^2}{2\left(x-y\right)\left(x+y\right)}-\dfrac{\left(x-y\right)^2}{2\left(x-y\right)\left(x+y\right)}+\dfrac{4y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{\left(x+y\right)^2-\left(x-y\right)^2+4y^2}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{4xy+4y^2}{2\left(x-y\right)\left(x+y\right)}=\dfrac{4y\left(x+y\right)}{2\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{2y}{x-y}\)
c.
\(\dfrac{x+5}{2x-4}.\dfrac{4-2x}{x+2}=\dfrac{x+5}{2x-4}.\dfrac{-\left(2x-4\right)}{x+2}=-\dfrac{x+5}{x+2}\)
d.
\(\dfrac{8}{x^2+2x-3}+\dfrac{2}{x+3}+\dfrac{1}{x-1}=\dfrac{8}{\left(x-1\right)\left(x+3\right)}+\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}+\dfrac{x+3}{\left(x-1\right)\left(x+3\right)}\)
\(=\dfrac{8+2\left(x-1\right)+x+3}{\left(x-1\right)\left(x+3\right)}=\dfrac{3x+9}{\left(x-1\right)\left(x+3\right)}\)
\(=\dfrac{3\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}=\dfrac{3}{x-1}\)
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Thực hiện phép tính:
\(a,\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(b,\left(\dfrac{2}{x^2-1}+\dfrac{x^2-3}{3x^2-1}\right):\left[\dfrac{1}{x}-\dfrac{2x\left(x^2-3\right)}{\left(x^2-1\right)\left(3x^2-1\right)}\right]\)