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NH
1
H
5 tháng 10 2023
\(A,xy\left(2x^2-3\right)-x^2\left(5xy+y\right)+x^2y\\ =2x^3y-3xy-5x^3y-x^2y+x^2y\\ =\left(2x^3y-5x^3y\right)+\left(-x^2y+x^2y\right)-3xy\\ =-3x^3y-3xy\)
\(B,3xyz\left(y-2\right)-5yz\left(1-y\right)-8z\left(y^2-3\right)\\ =3xy^2z-6xyz-5yz+5y^2z-8y^2z+24z\\ =3xy^2z-6xyz+\left(5y^2z-8y^2z\right)-5yz+24z\\ =3xy^2z-6xyz-3y^2z-5yz+24z\)
17 tháng 4 2021
Ta có: \(\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{x^3-y^3}-2+\dfrac{y}{y-x}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{2\left(x^3-y^3\right)-y\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\dfrac{2x^3+x^2y-xy^2-2x^3+2y^3-x^2y-xy^2-y^3}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}-\dfrac{y^3-2xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{y^2\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\cdot\dfrac{x}{x-y}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x^2-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x^3-xy^2+xy^2-x^3-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
10 tháng 8 2019
\(A=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x-2\right)\left(x^2+2x+4\right).\)
\(=x^3+y^3-\left(x^3-8\right)\)
\(=y^3+8\)
H
25 tháng 9 2023
\(A=x^2\left(x-y^2\right)-xy\left(1-xy\right)-x^3\\ =x^3-x^2y^2-xy+x^2y^2-x^3\\ =\left(x^3-x^3\right)+\left(-x^2y^2+x^2y^2\right)-xy\\ =-xy\)
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 12 2022
\(A=\dfrac{2x}{x\left(x+y\right)}+\dfrac{6x}{\left(x-y\right)\left(x+y\right)}-\dfrac{3}{x-y}\)
\(=\dfrac{2\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}+\dfrac{6x}{\left(x-y\right)\left(x+y\right)}-\dfrac{3\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}\)
\(=\dfrac{2x-2y+6x-3x-3y}{\left(x-y\right)\left(x+y\right)}=\dfrac{5\left(x-y\right)}{\left(x-y\right)\left(x+y\right)}\)
\(=\dfrac{5}{x+y}\)
\(\frac{xy+2x-y-2}{xy-x-y+1}=\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)+\left(1-x\right)}\)
\(=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)
\(\frac{\left(xy-y\right)+\left(2x-2\right)}{\left(xy-y\right)-\left(x-1\right)}=\frac{y\left(x-1\right)+2\left(x-1\right)}{y\left(x-1\right)-\left(x-1\right)}=\frac{\left(x-1\right)\left(y+2\right)}{\left(x-1\right)\left(y-1\right)}=\frac{y+2}{y-1}\)