Thực hiện phép tính
\(\left(\frac{x^2-y^2}{xy}-\frac{1}{x+y}\left(\frac{x^2}{y}-\frac{y^2}{x}\right)\right):\frac{x-y}{x}\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
29 tháng 10 2019
\(b.=\frac{1\left(c-a\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}+\frac{1\left(a-b\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}+\frac{1\left(b-c\right)}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=\frac{1c-1a+1a-1b+1b-1c}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
\(=-\frac{2b}{\left(a-b\right)\left(b-c\right)\left(c-a\right)}\)
14 tháng 11 2022
\(=\left[\dfrac{\left(x-y\right)\left(x+y\right)}{xy}-\dfrac{1}{x+y}\cdot\dfrac{x^3-y^3}{x-y}\right]\cdot\dfrac{x}{x-y}\)
\(=\left(\dfrac{x^2-y^2}{xy}-\dfrac{x^2+y^2+xy}{x+y}\right)\cdot\dfrac{x}{x-y}\)
\(=\dfrac{x^3+x^2y-xy^2-y^3-x^3y-xy^3-x^2y^2}{\left(x+y\right)\cdot xy}\cdot\dfrac{x}{x-y}\)
\(=\dfrac{x^3+x^2y-xy^2-y^3-x^3y-xy^3-x^2y^2}{y\left(x+y\right)\left(x-y\right)}\)
8 tháng 10 2018
\(\frac{x^2-yz}{\left(x+y\right)\left(x+z\right)}+\frac{y^2-xz}{\left(x+y\right)\left(y+z\right)}+\frac{z^2-xy}{\left(x+z\right)\left(y+z\right)}\)
\(=\frac{\left(x^2-yz\right).\left(y+z\right)}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}+\frac{\left(y^2-xz\right).\left(x+z\right)}{\left(x+y\right)\left(y+z\right)\left(x+z\right)}+\frac{\left(z^2-xy\right).\left(x+y\right)}{\left(x+z\right)\left(y+z\right)\left(x+y\right)}\)
\(=\frac{x^2y-y^2z+x^2z-yz^2+y^2x-x^2z+zy^2-xz^2+z^2x-x^2y+yz^2-xy^2}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}\)
\(=\frac{0}{\left(x+y\right)\left(x+z\right)\left(y+z\right)}\)
\(=0\)\(\left(\text{Đ}K:x+y,y+z,z+x\ne0\right)\)
Tham khảo nhé~
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
\(\frac{3xy^2+x^2y}{xy\left(x-y\right)}-\frac{3x^2y+xy^2}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y}{xy\left(x-y\right)}+\frac{-\left(3x^2y+xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy^2+x^2y-3x^2y-xy^2}{xy.\left(x-y\right)}\)
\(=\frac{\left(3xy^2-3x^2y\right)+\left(x^2y-xy^2\right)}{xy.\left(x-y\right)}\)
\(=\frac{3xy.\left(y-x\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy.\left(x-y\right)+xy.\left(x-y\right)}{xy.\left(x-y\right)}\)
\(=\frac{\left(x-y\right).\left(-3xy+xy\right)}{xy.\left(x-y\right)}\)
\(=\frac{-3xy+xy}{xy}\)
\(=\frac{-2xy}{xy}\)
\(=-2.\)
ĐK: \(x,y\ne0,x\ne\pm y\)
Phép tính trên bằng:
\(\left(\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{1}{x+y}.\frac{x^3-y^3}{xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x+y\right)^2}{xy\left(x+y\right)}-\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{\left(x+y\right)xy}\right):\frac{x-y}{x}\)
\(=\left(\frac{\left(x-y\right)\left(x^2+2xy+y^2-x^2-xy-y^2\right)}{xy\left(x+y\right)}\right):\frac{x-y}{x}\)
\(=\frac{\left(x-y\right)xy}{xy\left(x+y\right)}.\frac{x}{x-y}=\frac{x}{x+y}\)