a,(2x-1)(y+1)=14
b, xy=x+y
c, xy=x-y
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a: =(xy-2x)-(y^2-2y)
=x(y-2)-y(y-2)
=(x-y)(y-2)
b: =(x^2-2xy+y^2)-(x-y)
=(x-y)^2-(x-y)
=(x-y)(x-y-1)
c: =(x^2-1)-(2xy-2y)
=(x-1)(x+1)-2y(x-1)
=(x-1)(x+1-2y)
d: =(x+3)(x+3-2x+5)
=(x+3)(8-x)
\(a,xy-2x-y^2+2y\)
\(=x\left(y-2\right)-y\left(y-2\right)\)
\(=\left(x-y\right)\left(y-2\right)\)
\(b,x^2-2xy+y^2-x+y\)
\(=\left(x-y\right)^2-\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-1\right)\)
\(c,x^2-1-2xy+2y\)
\(=\left(x-1\right)\left(x+1\right)-2y\left(x-1\right)\)
\(=\left(x-1\right)\left(x+1-2y\right)\)
\(d,\left(x+3\right)^2-\left(2x-5\right)\left(x+3\right)\)
\(=\left(x+3\right)\left(x+3-2x+5\right)\)
\(=\left(x+3\right)\left(-x+8\right)\)
#Urushi
b: \(\dfrac{x^2y}{x-y}-\dfrac{xy^2}{x-y}\)(ĐKXĐ: x<>y)
\(=\dfrac{x^2y-xy^2}{x-y}\)
\(=\dfrac{xy\left(x-y\right)}{x-y}=xy\)
c: \(\dfrac{2x}{2x+y}+\dfrac{y}{y-2x}\)(ĐKXĐ: \(y\ne\pm2x\))
\(=\dfrac{2x}{2x+y}-\dfrac{y}{2x-y}\)
\(=\dfrac{2x\left(2x-y\right)-y\left(2x+y\right)}{\left(2x+y\right)\left(2x-y\right)}\)
\(=\dfrac{4x^2-2xy-2xy-y^2}{\left(2x+y\right)\left(2x-y\right)}=\dfrac{4x^2-4xy-y^2}{4x^2-y^2}\)