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Đặt B\(=\frac{y^2}{\left(x-y\right)^2}-\frac{2x^2y}{\left(x^2-y^2\right)^2}+\frac{x^2}{\left(y^2-x^2\right)}\)
\(B=\frac{y^2}{\left(x-y\right)^2}-\frac{2x^2y}{\left[\left(x-y\right)\left(x+y\right)\right]^2}-\frac{x^2}{\left(x-y\right)\left(x+y\right)}\) (làm tắt đấy x^2/(y^2 - x^2) = - x^2 /(x^2 - y^2)
Thay x + y = 1 vào B ta có
\(B=\frac{y^2}{\left(x-y\right)^2}-\frac{2x^2y}{\left(x-y\right)^2}-\frac{x^2}{x-y}\)
\(B=\frac{y^2-2x^2y-x^2\left(x-y\right)}{\left(x-y\right)^2}=\frac{y^2-x^2y-x^3}{\left(x-y\right)^2}\)
A = \(\frac{y-x}{xy}:B=\frac{y-x}{xy}\cdot\frac{\left(x-y\right)^2}{\left(y^2-x^2y-x^3\right)}=\frac{\left(x-y\right)^3}{-xy\left(y^2-x^2y-x^3\right)}\)
Sorry mình không giúp đc bạn
a) Rút gọn :
Ta có : \(A=\frac{y-x}{xy}:\left[\frac{y^2}{\left(x-y\right)^2}-\frac{2x^2y}{\left(x^2-y^2\right)^2}+\frac{x^2}{y^2-x^2}\right]\)
\(=\frac{y-x}{xy}:\left[\frac{y^2\left(x+y\right)^2-2x^2y-x^2\left(x^2-y^2\right)}{\left(x^2-y^2\right)^2}\right]\)
\(=\frac{y-x}{xy}:\left[\frac{y^2\left(x^2+2xy+y^2\right)-2x^2y-x^4+x^2y^2}{\left(x^2-y^2\right)^2}\right]\)
...
\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-2xy+xy-2y^2}\right):\dfrac{\left(2x^2+y\right)^2-4}{x\left(x+y\right)+\left(x+y\right)}:\dfrac{x+y}{2x^2+y+2}\)
\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{\left(x-2y\right)\left(x+y\right)}\right)\cdot\dfrac{\left(x+y\right)\left(x+1\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\cdot\dfrac{2x^2+y+2}{x+y}\)
\(=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}\)
\(=\dfrac{-\left(2x^2+y-2\right)}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(x+y\right)}\)
