\(P=\dfrac{1}{1+x+xy+xyz}+\dfrac{x}{x+xy+xyz+xyzt}+\)

\(\dfrac{xy}{xy+xyz+xyzt+xyzt\cdot x}+\dfrac{xyz}{xyz+xyzt+xyzt\cdot x+xyzt\cdot xy}\)

\(P=\dfrac{1}{1+x+xy+xyz}+\dfrac{x}{x+xy+xyz+1}+\)

\(\dfrac{xy}{xy+xyz+1+x}+\dfrac{xyz}{xyz+1+x+xy}\) ( do xyzt = 1 )

\(P=\dfrac{1+x+xy+xyz}{1+x+xy+xyz}=1\)

Thay xyzt = 1 vào P, có:

P= \(\frac{x}{xyz+xy+x+xyzt\ }\) + \(\frac{y}{yzt+yz+y+1}+\frac{z}{xzt+zt+z+xyzt}+\frac{t}{xyt+tx+t+1}\)

\(P=\frac{x}{x.\left(yz+y+1+yzt\right)}+\frac{y}{yzt+yz+y+1}+\frac{z}{z.\left(xt+t+1+xyt\right)}+\frac{t}{xyt+tx+t+1}\)

\(P=\frac{1\ +y}{yz+y+yzt+1}\) \(+\frac{1+t}{xyt+tx+t+1}\)

\(P=\frac{1+y}{yz+y+yzt+xyzt\ }+\frac{1+t}{xyt+tx+t+1}\)

\(P=\frac{1+y}{y.z.\left(xyt+tx+t+1\right)}+\frac{yz+tyz}{yz.\left(xyt+tx+t+1\right)}\)

\(P=\frac{1+y+yz+tyz}{yz.\left(xyt+tx+t+1\right)}=\frac{1+y+yz+tyz}{xyzt.\left(1+y+yz+tyz\right)}=\frac{1}{xyzt}=1\)

KL: P = 1 tại xyzt=1

\(\dfrac{x}{xyz+xy+x+1}+\dfrac{y}{yzt+yz+y+1}+\dfrac{z}{xzt+zt+z+1}+\dfrac{t}{xyt+tx+t+1}\)

= \(\dfrac{x}{xyz+xy+x+1}+\dfrac{xy}{xyzt+xyz+xy+x}+\dfrac{xyz}{x^2yzt+xyzt+xyz+xy}+\dfrac{xyzt}{x^{2^{ }}y^2zt+x^2yzt+xyzt+xyz}\)

= \(\dfrac{x}{xyz+xy+x+1}+\dfrac{xy}{1+xyz+xy+x}+\dfrac{xyz}{x+1+xyz+xy}+\dfrac{1}{xy+x+1+xyz}\)

= \(\dfrac{x+xy+xyz+1}{x+xy+xyz+1}\)

= 1