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\(a,\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}:\left(\frac{1}{x}+\frac{1}{y}\right)\)
\(=\left(\frac{x}{y\left(x-y\right)}+\frac{y-2x}{x\left(x-y\right)}\right):\left(\frac{y}{xy}+\frac{x}{xy}\right)\)
\(=\left(\frac{x-y}{x\left(x-y\right)}\right):\left(\frac{x+y}{xy}\right)\)
\(=\frac{1}{x}.\frac{xy}{x+y}=\frac{y}{x+y}\)
a: \(=\left(\dfrac{x}{y\left(x-y\right)}-\dfrac{2x-y}{x\left(x-y\right)}\right):\dfrac{x+y}{xy}\)
\(=\dfrac{x^2-2xy+y^2}{xy\left(x-y\right)}\cdot\dfrac{xy}{x+y}\)
\(=\dfrac{\left(x-y\right)^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{x-y}{x+y}\)
b: \(=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2+4y^2}{2\left(x-y\right)\left(x+y\right)}\cdot\dfrac{x-y}{2y}\)
\(=\dfrac{4xy+4y^2}{2\left(x+y\right)}\cdot\dfrac{1}{2y}=\dfrac{4y\left(x+y\right)}{4y\left(x+y\right)}=1\)
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: \(=\dfrac{x^3-1}{x-1}-\dfrac{x^2-1}{x+1}\)
\(=x^2+x+1-x+1=x^2+2\)
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: \(=\dfrac{1}{x-1}-\dfrac{x\left(x-1\right)\left(x+1\right)}{x^2+1}\cdot\left(\dfrac{x+1-x+1}{\left(x-1\right)^2\cdot\left(x+1\right)}\right)\)
\(=\dfrac{1}{x-1}-\dfrac{x}{x^2+1}\cdot\dfrac{2}{\left(x-1\right)}=\dfrac{x^2+1-2x}{\left(x-1\right)\left(x^2+1\right)}=\dfrac{x-1}{x^2+1}\)
\(P=\dfrac{2}{x}-\left(\dfrac{x^2y}{xy\left(x-y\right)}+\dfrac{\left(x^2-y^2\right)\left(x-y\right)}{xy\left(x-y\right)}+\dfrac{xy^2}{xy\left(x-y\right)}\right).\dfrac{x-y}{x^2-xy+y^2}\)
\(P=\dfrac{2}{x}-\left(\dfrac{x^2y+x^3-x^2y-xy^2+y^3+xy^2}{x\left(x-y\right)}\right).\dfrac{x-y}{x^2-xy+y^2}\)\(P=\dfrac{2}{x}-\dfrac{x^3+y^3}{x\left(x-y\right)}.\dfrac{x-y}{x^2-xy+y^2}=\dfrac{2}{x}-\dfrac{\left(x-y\right)\left(x^2-xy+y^2\right)}{x\left(x-y\right)}.\dfrac{x-y}{x^2-xy+y^2}=\dfrac{2}{x}-\dfrac{x-y}{x}=\dfrac{2-x-y}{x}\)Vậy \(P=\dfrac{2-x-y}{x}\)
a. Để x , y xác định thì \(x\ne0\) ; x2 - xy khác 0 ; y2 - xy khác 0 ; x - y khác 0
=> x khác 0; x(x-y) khác 0; xy khác 0 ; y(y-x) khác 0
* Với x(x-y) khác 0 => x khác 0 hoặc x - y khác 0
=> x khác 0 hoặc x khác y
* y(y-x) khác 0 suy ra y khác 0 hoặc y - x khác 0
=> x khác y
Vậy để P xác định thì x và y khác 0 ; và x khác y