Bài 3 ( 3đ) : Thực hiện phép tính
\(\dfrac{y}{x-y}-\dfrac{x^3-xy^2}{x^2+y^2}.\left(\dfrac{x}{x^2-2xy+y^2}-\dfrac{y}{x^2-y^2}\right)\)
17 tháng 2 2021 lúc 13:05
Ta có: \(\dfrac{y}{x-y}-\dfrac{x^3-xy^2}{x^2+y^2}\cdot\left(\dfrac{x}{x^2-2xy+y^2}-\dfrac{y}{x^2-y^2}\right)\)
\(=\dfrac{y}{x-y}-\dfrac{x\left(x^2-y^2\right)}{x^2+y^2}\cdot\left(\dfrac{x\left(x+y\right)}{\left(x-y\right)^2\cdot\left(x+y\right)}-\dfrac{y\cdot\left(x-y\right)}{\left(x-y\right)^2\cdot\left(x+y\right)}\right)\)
\(=\dfrac{y}{x-y}-\dfrac{x\left(x-y\right)\left(x+y\right)}{x^2+y^2}\cdot\dfrac{x^2+xy-xy+y^2}{\left(x-y\right)^2\left(x+y\right)}\)
\(=\dfrac{y}{x-y}-\dfrac{x\cdot\left(x^2+y^2\right)}{\left(x^2+y^2\right)\cdot\left(x-y\right)}\)
\(=\dfrac{y}{x-y}-\dfrac{x}{x-y}\)
\(=\dfrac{y-x}{x-y}=\dfrac{-\left(x-y\right)}{x-y}=-1\)
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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 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 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 , 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 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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cm đẳng thức\(a.\dfrac{x}{x+y}+\dfrac{4}{x^2+3xy+2y^2}+\dfrac{-3x}{x+2y}=\dfrac{-2x^2-xy+4}{\left(x+y\right)\left(x+2y\right)}\) với x ≠ -y; x ≠ -2y
b. \(\dfrac{x+y}{x-y}=\dfrac{x^2+2xy+y^2}{x^2-y^2}\)
\(a,VT=\dfrac{x^2+2xy+4-3x^2-3xy}{\left(x+y\right)\left(x+2y\right)}=\dfrac{-2x^2-xy+4}{\left(x+y\right)\left(x-2y\right)}=VP\\ b,VP=\dfrac{\left(x+y\right)^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{x+y}{x-y}=VT\)
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thuc hien phep tinh
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}+1-2right)
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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thuc hien phep tinh
a.\(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
b.\(\left(\dfrac{1}{x^2+1}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+1-2\right)\)
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: \(=\dfrac{4x^2+4x+1-\left(4x^2-4x+1\right)}{\left(2x-1\right)\left(2x+1\right)}\cdot\dfrac{5\left(2x-1\right)}{4x}\)
\(=\dfrac{8x}{2x+1}\cdot\dfrac{5}{4x}=\dfrac{10}{2x+1}\)
c: \(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)}{x^2+1}\cdot\left(\dfrac{x+1-x+1}{\left(x-1\right)^2\cdot\left(x+1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x}{x^2+1}\cdot\dfrac{2}{\left(x-1\right)}=\dfrac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}=\dfrac{x-1}{x^2+1}\)
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cho 2 số thực `x,y` thỏa mãn `x>0,y>2,x`\(\ne\)`2y`. CMR: \(\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right)\left(2x^2+y+2\right):\dfrac{x^4+4x^2y^2+y^4-4}{x^2+y+xy+x}=\dfrac{x+1}{2y-x}\)
Đề bài sai, đề đúng thì phân thức đằng sau dấu chia phải là:
\(\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
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Thực hiện phép tính:
a) dfrac{1}{x-y}+dfrac{3xy}{y^3-x^3}+dfrac{x-y}{x^2+xy+y^2}
b) dfrac{2x+y}{2x^2-xy}+dfrac{16x}{y^2-4x^2}+dfrac{2x-y}{2x^2+xy}
c) dfrac{xy}{ab}+dfrac{left(x-aright)left(y-aright)}{aleft(a-bright)}-dfrac{left(x-bright)left(y-bright)}{bleft(a-bright)}
d) dfrac{x^3}{x-1}-dfrac{x^2}{x+1}-dfrac{1}{x-1}+dfrac{1}{x+1}
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Thực hiện phép tính:
a) \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\)
b) \(\dfrac{2x+y}{2x^2-xy}+\dfrac{16x}{y^2-4x^2}+\dfrac{2x-y}{2x^2+xy}\)
c) \(\dfrac{xy}{ab}+\dfrac{\left(x-a\right)\left(y-a\right)}{a\left(a-b\right)}-\dfrac{\left(x-b\right)\left(y-b\right)}{b\left(a-b\right)}\)
d) \(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
a: \(=\dfrac{1}{x-y}-\dfrac{3xy}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{x-y}{x^2+xy+y^2}\)
\(=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{2x^2-4xy+2y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}\)
d: \(=\dfrac{x^3-1}{x-1}-\dfrac{x^2-1}{x+1}\)
\(=x^2+x+1-x+1=x^2+2\)
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