Thực hiện phép tính: \(\frac{x+y}{y-x}:\frac{x^2+xy}{3x^2-3y^2}\)
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TT
2 tháng 9 2020
\(ĐKXĐ:x\ne y,x\ne0,y\ne0\)
Ta có : \(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}=\frac{-2xy.\left(x-y\right)}{xy.\left(x-y\right)}=-2\)
VM
2 tháng 9 2020
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y}{xy\left(x-y\right)}+\frac{-\left(3x^2y+xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{\left(3xy^2-3x^2y\right)+\left(x^2y-xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy.\left(y-x\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{\left(x-y\right).\left(-3xy+xy\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy+xy}{xy}\)
\(=\frac{-2xy}{xy}\)
\(=-2.\)
30 tháng 10 2018
ĐK: \(x,y\ne0,x\ne\pm y\)
Phép tính trên bằng:
\(\left(\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{1}{x+y}.\frac{x^3-y^3}{xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x+y\right)^2}{xy\left(x+y\right)}-\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x^2+2xy+y^2-x^2-xy-y^2\right)}{xy\left(x+y\right)}\right):\frac{x-y}{x}\)
\(=\frac{\left(x-y\right)xy}{xy\left(x+y\right)}.\frac{x}{x-y}=\frac{x}{x+y}\)
22 tháng 7 2023
`a)`
`3x(2xy - 5x^2y)`
`= 3x*2xy + 3x* (-5x^2y)`
`= 6x^2y - 15x^3y`
`b)`
`2x^2y (xy - 4xy^2 + 7y)`
`= 2x^2y * xy + 2x^2y * (-4xy^2) + 2x^2y * 7y`
`= 2x^3y^2 - 8x^3y^3 + 14x^2y^2`
`c)`
`(-2/3xy^2 + 6yz^2)*(-1/2xy)`
`= (-2/3xy^2)*(-1/2xy) + 6yz^2 * (-1/2xy)`
`= 1/3x^2y^3 - 3xy^2z^2`
22 tháng 7 2023
`a, 3x(2xy-5x^2y)`
`= 6x^2y - 15x^3y`
`b, 2x^2y(xy-4xy^2+7y)`
`= 2x^3y^2 - 8x^3y^3 + 14x^2y^2`
`c, (-2/3xy^2 + 6yz^2).(-1/2xy)`
`= 1/3x^2y^3 - 3xy^2z^2`
26 tháng 12 2020
a. 2x(x + y) - y(y + 2x) = 2x2 + 2xy - y2 - 2xy = 2x2 - y2
b.\(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
Phần c nản quá.
XO
25 tháng 12 2020
a) 2x(x + y) - y(y + 2x)
= 2x2 + 2xy - y2 - 2xy
= 2x2 - y2
b) \(\frac{4x+3y}{7x^2y}-\frac{3x+3y}{7x^2y}=\frac{4x+3y-3x-3y}{7x^2y}=\frac{x}{7x^2y}=\frac{1}{7xy}\)
c) \(\frac{x^3-4x^2}{x^3-1}+\frac{2}{x^2+x+1}+\frac{1}{x-1}\)
= \(\frac{x^3-4x^2}{\left(x-1\right)\left(x^2+x+1\right)}+\frac{2\left(x-1\right)}{\left(x^2+x+1\right)\left(x-1\right)}+\frac{x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}\)
= \(\frac{x^3-4x^2+2x-2+x^2+x+1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{x^3-3x^2+3x-1}{\left(x^2+x+1\right)\left(x-1\right)}=\frac{\left(x-1\right)^3}{\left(x^2+x+1\right)\left(x-1\right)}\)
\(=\frac{\left(x-1\right)^2}{x^2+x+1}\)
2 tháng 12 2023
Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
M
1
4 tháng 8 2023
\(\dfrac{xy}{x-y}-\dfrac{2x^2}{y-2x}\)
\(=\dfrac{xy}{x-y}+\dfrac{2x^2}{2x-y}\)
\(=\dfrac{xy\left(2x-y\right)+2x^2\left(x-y\right)}{\left(x-y\right)\left(2x-y\right)}\)
\(=\dfrac{2x^2y-xy^2+2x^3-2x^2y}{\left(x-y\right)\left(2x-y\right)}\)
\(=\dfrac{2x^3-xy^2}{\left(x-y\right)\left(2x-y\right)}=\dfrac{x\left(2x^2-y^2\right)}{\left(x-y\right)\left(2x-y\right)}\)
