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\(\dfrac{\left(x+y\right)2}{x2+xy}+\dfrac{\left(x-y\right)2}{x2-xy}=-\left(\dfrac{\left(x-y\right)2}{x2-xy}\right)+\dfrac{\left(x-y\right)2}{x2-xy}=0\)
b: \(\dfrac{x^2-4x}{xy-4x-3y+12}+\dfrac{x-2}{y-4}\)
\(=\dfrac{x\left(x-4\right)}{\left(y-4\right)\left(x-3\right)}+\dfrac{x-2}{y-4}\)
\(=\dfrac{x^2-4x+x^2-5x+6}{\left(y-4\right)\left(x-3\right)}=\dfrac{2x^2-9x+6}{\left(y-4\right)\left(x-3\right)}\)
c: \(=\dfrac{y^2}{\left(y-5\right)\left(x+1\right)}+\dfrac{2}{x+1}\)
\(=\dfrac{y^2+2y-10}{\left(y-5\right)\left(x+1\right)}\)
a, \(\dfrac{x+1}{3}+\dfrac{2x-1}{3}=\dfrac{x+1+2x-1}{3}=\dfrac{3x}{3}=x\)
b, \(\dfrac{5x-2y}{x^2-y^2}+\dfrac{y-4x}{x^2-y^2}=\dfrac{5x-2y+y-4x}{\left(x+y\right)\left(x-y\right)}=\dfrac{x-y}{\left(x+y\right)\left(x-y\right)}=\dfrac{1}{x+y}\)
c, \(\dfrac{x-1}{12x}+\dfrac{2x+7}{12x}+\dfrac{6-3x}{12x}=\dfrac{x-1+2x+7+6-3x}{12x}=\dfrac{12}{12x}=\dfrac{1}{x}\)
a,\(\dfrac{x+1_{ }+2x-1}{3}\)=\(\dfrac{2x}{3}\)
b,\(\dfrac{5x-2y+y-4x}{\left(x+y\right)\left(x-y\right)}\)=\(\dfrac{x-y}{\left(x+y\left(x-y\right)\right)}\)
c,\(\dfrac{x-1+2x+7+6-3x}{12x}\)=\(\dfrac{12}{12x}\)=\(\dfrac{1}{x}\)
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
`1)(x-2y)(x^2+2xy+4xy^2)-(x^3-8y^3+1)`
`=(x-2y)(x^2+2xy+4xy^2)-[(x^3-(2y)^3)+1]`
`=(x-2y)(x^2+2xy+4xy^2)-(x-2y)(x^2+2xy+4y^2)-1`
`=(x-2y)(x^2+2xy+4xy^2-x^2-2xy-4y^2)-1`
`=(x-2y)(4xy^2-4y^2)-1`
`=x(4xy^2-4y^2)-2y(4xy^2-4y^2)-1`
`=4x^2y^2-4xy^2-8xy^3+8y^3-1`
`2)y(x^2-y^2)+x(y^2-x^2)xy(x+y)`
`=x^2y-y^3+(xy^2-x^3)(x^2y+xy^2)`
`=x^2y-y^3+xy^2(x^2y+xy^2)-x^3(x^2y+xy^2)`
`=x^2y-y^3+x^3y^3+x^2y^4-x^5y-x^4y^2`
`3)(x+y)(x-2y)-x(x-y)+y^2`
`=x(x-2y)+y(x-2y)-(x^2-xy)+y^2`
`=x^2-2xy+xy-2y^2-x^2+xy+y^2`
`=(x^2-x^2)+(-2xy+xy+xy)+(-2y^2+y^2)`
`=-y^2`