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a)\(\dfrac{2x^2-10xy}{2xy}+\dfrac{5y-x}{y}+\dfrac{x+2y}{x}\)
\(=\dfrac{2x\left(x-5y\right)}{2xy}+\dfrac{5y-x}{y}+\dfrac{x+2y}{x}\)
\(=\dfrac{x-5y}{y}+\dfrac{5y-x}{y}+\dfrac{x+2y}{x}\)
\(=\dfrac{x\left(x-5y\right)+x\left(5y-x\right)+y\left(x+2y\right)}{xy}\)
\(=\dfrac{x^2-5xy+5xy-x^2+xy+2y^2}{xy}\)
\(=\dfrac{y\left(x+2y\right)}{xy}\)
b) \(\dfrac{x+1}{2x-2}+\dfrac{x^2+3}{2-2x^2}\)
\(=\dfrac{x+1}{2x-2}-\dfrac{x^2+3}{2x^2-2}\)
\(=\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x^2+3}{2\left(x^2-1\right)}\)
\(=\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x^2+3}{2\left(x-1\right)\left(x+1\right)}\) MTC: \(2\left(x-1\right)\left(x+1\right)\)
\(=\dfrac{\left(x+1\right)\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}-\dfrac{x^2+3}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x+1\right)-\left(x^2+3\right)}{2\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)^2-x^2-3}{2\left(x-1\right)\left(x+1\right)}\)
e) \(\dfrac{2x^2-xy}{x-y}+\dfrac{xy+y^2}{y-x}+\dfrac{2y^2-x^2}{x-y}\)
\(=\dfrac{2x^2-xy}{x-y}-\dfrac{xy+y^2}{x-y}+\dfrac{2y^2-x^2}{x-y}\)
\(=\dfrac{\left(2x^2-xy\right)-\left(xy+y^2\right)+\left(2y^2-x^2\right)}{x-y}\)
\(=\dfrac{2x^2-xy-xy-y^2+2y^2-x^2}{x-y}\)
\(=\dfrac{x^2-2xy+y^2}{x-y}\)
\(=\dfrac{\left(x-y\right)^2}{x-y}\)
\(=x-y\)
1. \(\dfrac{x^3-4x^2+4x}{x^2-4}=\dfrac{x\left(x^2-4x+4\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{x\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}=\dfrac{x\left(x-2\right)}{x+2}\)
\(VT=\dfrac{x^2+xy+2xy+2y^2}{x^2\left(x+2y\right)-y^2\left(x+2y\right)}=\dfrac{\left(x+y\right)\left(x+2y\right)}{\left(x+2y\right)\left(x-y\right)\left(x+y\right)}=\dfrac{1}{x-y}\)
B) Ta có: 2x-2y-x2+2xy-y2
⇔ 2(x-y)-(x2-2xy+y2)
⇔ 2(x-y)-(x-y)2
⇔ (x-y)(2-x+y)
Đúng thì tick nhé
a: \(=\dfrac{2x^2+2xy-xy-y^2}{2x^2-2xy-xy+y^2}=\dfrac{\left(x+y\right)\left(2x-y\right)}{\left(x-y\right)\left(2x-y\right)}=\dfrac{x+ỹ}{x-y}\)
b: Sửa đề:\(\dfrac{\left(x+y\right)^2}{2y^2+xy-x^2}\)
\(=\dfrac{\left(x+y\right)^2}{2y^2+2xy-xy-x^2}\)
\(=\dfrac{\left(x+y\right)^2}{\left(x+y\right)\left(2y-x\right)}=\dfrac{x+y}{2y-x}\)
\(\dfrac{x^4-xy^3}{2xy+y^2}:\dfrac{x^3+x^2y+xy^2}{2x+y}\)
\(=\dfrac{x\left(x^3-y^3\right)}{y\left(2x+y\right)}:\dfrac{x\left(x^2+xy+y^2\right)}{2x+y}\)
\(=\dfrac{x\left(x-y\right)\left(x^2+xy+y^2\right)}{y\left(2x+y\right)}:\dfrac{x\left(x^2+xy+y^2\right)}{2x+y}\)
\(=\dfrac{x\left(x-y\right)\left(x^2+xy+y^2\right)\left(2x+y\right)}{y\left(2x+y\right)x\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x-y}{y}\)
ĐKXĐ: \(x,y\ne0;x\ne-\dfrac{1}{2}y\)
\(\dfrac{x^4-xy^3}{2xy+y^2}:\dfrac{x^3+x^2y+xy^2}{2x+y}\)
\(=\dfrac{x\left(x^3-y^3\right)}{y.\left(2x+y\right)}:\dfrac{x\left(x^2+xy+y^2\right)}{2x+y}\)
\(=\dfrac{x\left(x-y\right)\left(x^2+xy+y^2\right)}{y.\left(2x+y\right)}.\dfrac{2x+y}{x.\left(x^2+xy+y^2\right)}\)
\(=\dfrac{x-y}{y}\left(x;2x+y;x^2+xy+y^2\ne0\right)\)
\(=\dfrac{y\left(x^2+2xy+y^2\right)}{2x^2+2xy-xy-y^2}\)
\(=\dfrac{y\left(x+y\right)^2}{\left(x+y\right)\left(2x-y\right)}=\dfrac{y\left(x+y\right)}{2x-y}\)
\(=\dfrac{xy+y^2}{2x-y}\)