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a: =6xy+xy=7xy
b: =-9xy^2
c: =-x^2y^3z^4
d: =-4x^2y
e: =-30x^2y
f: =6x^2y
\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-2xy+xy-2y^2}\right):\dfrac{\left(2x^2+y\right)^2-4}{x\left(x+y\right)+\left(x+y\right)}:\dfrac{x+y}{2x^2+y+2}\)
\(=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{\left(x-2y\right)\left(x+y\right)}\right)\cdot\dfrac{\left(x+y\right)\left(x+1\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\cdot\dfrac{2x^2+y+2}{x+y}\)
\(=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}\)
\(=\dfrac{-\left(2x^2+y-2\right)}{\left(x-2y\right)\left(x+y\right)}\cdot\dfrac{x+1}{2x^2+y-2}=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(x+y\right)}\)
a) ĐKXĐ: \(x\ne2y,x\ne-y;x\ne-1\)
b) \(B=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
\(B=\left[\dfrac{y-x}{x-2y}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{4x^4+4x^2y+y^2-4}{x\left(x+y\right)+\left(x+y\right)}\)
\(B=\left[\dfrac{\left(y-x\right)\left(x+y\right)}{\left(x-2y\right)\left(x+y\right)}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x+y\right)\left(x-2y\right)}:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{-2x^2-y+2}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(2x^2+y-2\right)}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(2x^2+y+2\right)}\)
2y^2 +xy -x^2 =y(y+x) +y^2 -x^2 =(x+y)(2y-x)
4x^2 +4x^2 y +y^2 -4 =4x^2 (y+1) +y^2-4 có vẻ hệ số lệch lại nhỉ
x^2 +y +xy +x =x(x+y) +x+y =(x+y) (x+1)
\(B=\dfrac{x-y}{2y-x}+\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(2y-x\right)}=\dfrac{x^2-y^2+\left(x^2+y^2+y-2\right)}{\left(x+y\right)\left(2y-x\right)}=\dfrac{2x^2+y-2}{\left(x+y\right)\left(2y-x\right)}\)\(C=\dfrac{4x^2\left(y+1\right)+y^2-4}{\left(x+y\right)\left(x+1\right)}\)
\(A=B:C=\dfrac{2x^2+y-2}{\left(x+y\right)\left(2y-x\right)}.\dfrac{\left(x+y\right)\left(x+1\right)}{4x^2\left(y+1\right)+y^2-4}\)
\(A=\dfrac{2x^2+y-2}{\left(2y-x\right)}.\dfrac{\left(x+1\right)}{4x^2\left(y+1\right)+y^2-4}\)
a: A=-2xy+xy+xy^2=-xy+xy^2
Bậc là 3
b: \(B=xy^2z+2xy^2z-3xy^2z+xy^2z-xyz=-xyz+xy^2z\)
Bậc là 4
c: \(C=4x^2y^3-x^2y^3+x^4+6x^4-2x^2=3x^2y^3+7x^4-2x^2\)
Bậc là 5
d: \(D=\dfrac{3}{4}xy^2-\dfrac{1}{2}xy^2+xy=\dfrac{1}{4}xy^2+xy\)
bậc là 3
e: \(E=2x^2-4x^2+3z^4-z^4-3y^3+2y^3\)
=-2x^2+2z^4-y^3
Bậc là 4
f: \(=3xy^2z+xy^2z+2xy^2z-4xyz=6xy^2z-4xyz\)
Bậc là 4
\(x^2-xy+4x-2y+4\)
=\(\left(x+2\right)^2-y\left(x+2\right)\)
=\(\left(x+2\right)\left(x-y+2\right)\)