Đáp án \(+\) Giải thích :

  \(B=\dfrac{x-xy+3xy+1}{x+xy+xz+1}+\dfrac{y-yz+3yz+1}{y+yz+yx+1}+\dfrac{z-zy+3xy+1}{z+zx+zy+1}\)

  \(B=\dfrac{x + 2xy + 1}{x+xy+xz+1}+\dfrac{y + 2yz + 1}{y+yz+yx+1}+\dfrac{z-zy+3xy+1}{z+zx+zy+1}\)

  \(B=\dfrac{x + 2xy + 1}{x(1+y)(1+z)}+\dfrac{y + 2yz + 1}{y(1+z)(1+x)}+\dfrac{z-zy+3xy+1}{z(1+x)(1+y)}\)

  \(B=\dfrac{xyz+2xyz\cdot y+yz}{xyz(1+y)(1+z)}=\dfrac{xyz+2xyz\cdot z+xz}{xyz(1+z)(1+x)}=\dfrac{xyz-xyz\cdot y+3x^{2}y^{2}+xy}{xyz(1+x)(1+y)}\)

  \(B=\dfrac{1+2y+yz}{(1+y)(1+z)}=\dfrac{1+2z+xz}{(1+z)(1+x)}=\dfrac{1-y+3x^{2}y^{2}+xy}{(1+x)(1+y)}\)

  \(B=\dfrac{1+2y+yz}{(1+y)(1+z)}+\dfrac{1+2z+zx}{(1+z)(1+x)}+\dfrac{1+2x+xy}{(1+x)(1+y)}\)

  \(B=\dfrac{(1+2y+yz)(1+x)}{(1+x)(1+y)(1+z)}+\dfrac{(1+2z+zx)(1+y)}{(1+x)(1+y)(1+z)}+\dfrac{(1+2x+xy)(1+z)}{(1+x)(1+y)(1+z)}\)

  \(B=\dfrac{(1+x+2y+2xy+yz+xyz)+(1+y+2z+2yz+zx+xyz)+(1+z+2x+2zx+xy+xyz)}{(1+x)(1+y)(1+z)}\)

  \(B=\dfrac{(1+x+2y+2xy+yz+1)+(1+y+2z+2yz+zx+1)+(1+z+2x+2zx+xy+1)}{(1+x)(1+y)(1+z)}\)

  \(B=\dfrac{(x+2y+yz+2xy+2)+(y+2z+zx+2yz+2)+(z+2x+xy+2zx+2)}{(1+x)(1+y)(1+z)}\)

  \(B=\dfrac{3x+3y+3z+3xy+3yz+3zx+6}{(1+x)(1+y)(1+z)}\)

  \(B=\dfrac{3(x+y+z+xy+yz+zx+2)}{(1+x+y+xy)(1+z)}\)

  \(B=\dfrac{3(x+y+z+xy+yz+zx+2)}{1+z+x+xz+y+yz+xy+xyz}\)

  \(B=\dfrac{3(x+y+z+xy+yz+zx+2)}{1+z+x+xz+y+yz+xy+1}\)

  \(B=\dfrac{3(x+y+z+xy+yz+zx+2)}{x+y+z+xy+yz+zx+2}\)

 \(\Rightarrow \) \(B=3\)

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