Rút gọn (x^2-x-xy+y)/(xy-x-y^2+y)
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BP
1
10 tháng 10 2021
\(\left(x^2+xy+y^2\right)\left(x-y\right)-\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(=x^2-y^3-x^3-y^3=-2y^3\)
17 tháng 4 2021
Ta có: \(\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{x^3-y^3}-2+\dfrac{y}{y-x}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\left(\dfrac{x\left(2x^2+xy-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{2\left(x^3-y^3\right)-y\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\right):\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x^2+xy}{x^2+xy+y^2}-\dfrac{2x^3+x^2y-xy^2-2x^3+2y^3-x^2y-xy^2-y^3}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}-\dfrac{y^3-2xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}:\dfrac{x-y}{x}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{y^2\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\cdot\dfrac{x}{x-y}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x+y\right)}{x^2+xy+y^2}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x}{x-y}\)
\(=\dfrac{x\left(x^2-y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}+\dfrac{xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}-\dfrac{x\left(x^2+xy+y^2\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x^3-xy^2+xy^2-x^3-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
\(=\dfrac{-x^2y-xy^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)
A
0
TS
2
6 tháng 5 2022
gánh còng não :v
\(\left(\dfrac{\sqrt{y}}{x+\sqrt{y}}+\dfrac{\sqrt{y}}{x-\sqrt{xy}}\right):\dfrac{2\sqrt{xy}}{xy}=\left(\dfrac{\sqrt{y}}{x+\sqrt{y}}+\dfrac{\sqrt{y}}{\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)}\right):\dfrac{2}{\sqrt{xy}}=\dfrac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)+\sqrt{x}\left(x+\sqrt{y}\right)}{\sqrt{x}\left(x+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}:\dfrac{2}{\sqrt{xy}}=\dfrac{x\sqrt{y}-y\sqrt{x}+x\sqrt{x}+\sqrt{xy}}{\sqrt{x}\left(x+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}:\dfrac{2}{\sqrt{xy}}=\dfrac{\sqrt{x}\left(\sqrt{xy}-y+x+\sqrt{y}\right)}{\sqrt{x}\left(x+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}:\dfrac{2}{\sqrt{xy}}=\dfrac{\sqrt{y}\left(\sqrt{x}-\sqrt{y}\right)+\left(x+\sqrt{y}\right)}{\left(x +\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}:\dfrac{2}{\sqrt{xy}}\) mình làm đc đó thôi ( mỏi tay :v )
BT
24 tháng 3 2018
\(A=\left[\frac{x^2-y^2}{xy}-\frac{1}{xy}\left(\frac{x^2}{y}-\frac{y^2}{x}\right)\right]:\frac{x-y}{xy}\)
\(A=\left[\frac{x^2-y^2}{xy}-\left(\frac{x}{y^2}-\frac{y}{x^2}\right)\right].\frac{xy}{x-y}\) => \(A=\left(\frac{x^2-y^2}{xy}-\frac{x^3-y^3}{x^2y^2}\right).\frac{xy}{x-y}=\left(\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{\left(x-y\right)\left(x^2+xy+y^2\right)}{x^2y^2}\right).\frac{xy}{x-y}\)
=> \(A=\frac{x-y}{xy}\left(\left(x+y\right)-\frac{x^2+xy+y^2}{xy}\right).\frac{xy}{x-y}\)=> \(A=x+y-\frac{x^2+xy+y^2}{xy}=\frac{x^2y+xy^2-x^2-xy-y^2}{xy}\)
28 tháng 2 2020
Với đk trên ta có:
P = \(\frac{2}{x}-\left(\frac{x^2}{x^2+xy}+\frac{y^2-x^2}{xy}-\frac{y^2}{xy+y^2}\right).\frac{x+y}{x^2+xy+y^2}\)
\(=\frac{2}{x}-\left(\frac{x}{x+y}-\frac{\left(x-y\right)\left(x+y\right)}{xy}-\frac{y}{x+y}\right).\frac{x+y}{x^2+xy+y^2}\)
\(=\frac{2}{x}-\left(\frac{x-y}{x+y}-\frac{\left(x-y\right)\left(x+y\right)}{xy}\right).\frac{x+y}{x^2+xy+y^2}\)
\(=\frac{2}{x}-\frac{x-y}{xy}.\left(xy-\left(x+y\right)^2\right).\frac{1}{x^2+xy+y^2}\)
\(=\frac{2}{x}+\frac{x-y}{xy}\)
\(=\frac{x+y}{xy}\)
21 tháng 2 2021
1) Ta có: \(\dfrac{1}{7}x^2y^3\cdot\left(-\dfrac{14}{3}xy^2\right)\cdot\left(-\dfrac{1}{2}xy\right)\left(x^2y^4\right)\)
\(=\left(-\dfrac{1}{7}\cdot\dfrac{14}{3}\cdot\dfrac{-1}{2}\right)\left(x^2y^3\cdot xy^2\cdot xy\cdot x^2y^4\right)\)
\(=\dfrac{1}{3}x^6y^{10}\)
2) Ta có: \(\left(3xy\right)^2\cdot\left(-\dfrac{1}{2}x^3y^2\right)\)
\(=9xy^2\cdot\dfrac{-1}{2}x^3y^2\)
\(=-\dfrac{9}{2}x^4y^4\)
3) Ta có: \(\left(-\dfrac{1}{4}x^2y\right)^2\cdot\left(\dfrac{2}{3}xy^4\right)^3\)
\(=\dfrac{1}{16}x^4y^2\cdot\dfrac{8}{27}x^3y^{12}\)
\(=\dfrac{1}{54}x^7y^{14}\)
\(\frac{x^2-x-xy+y}{xy-x-y^2+y}\)
ĐKXĐ : \(\hept{\begin{cases}x\ne y\\y\ne1\end{cases}}\)
\(=\frac{\left(x^2-x\right)-\left(xy-y\right)}{\left(xy-x\right)-\left(y^2-y\right)}\)
\(=\frac{x\left(x-1\right)-y\left(x-1\right)}{x\left(y-1\right)-y\left(y-1\right)}\)
\(=\frac{\left(x-1\right)\left(x-y\right)}{\left(y-1\right)\left(x-y\right)}\)
\(=\frac{x-1}{y-1}\)
Bài làm
\(\frac{x^2-x-xy+y}{xy-x-y^2+y}=\frac{x\left(x-1\right)-y\left(x-1\right)}{x\left(y-1\right)-y\left(y-1\right)}=\frac{\left(x-1\right)\left(x-y\right)}{\left(x-y\right)\left(y-1\right)}\)
\(=\frac{x-1}{y-1}\)