Ответ:

[tex]\displaystyle 1[/tex]

Объяснение:

[tex]\displaystyle \frac{1}{1 + x + xy} + \frac{1}{1 + y + yz} + \frac{1}{1 + z + xz}=\\\\\frac{z}{z(1 + x + xy)} + \frac{1}{1 + y + yz} + \frac{1}{1 + z + xz}=\\\\\frac{z}{z + xz + 1} + \frac{1}{1 + z + xz}+ \frac{1}{1 + y + yz} =\\\\\frac{z +1}{1 + z + xz}+\frac{1}{1 + y + yz} =\\\\\frac{y(z +1)}{y(1 + z + xz)}+\frac{1}{1 + y + yz} =\\\\\frac{yz +y}{y + yz + xyz}+\frac{1}{1 + y + yz} =\\\\\frac{yz +y}{y + yz + 1}+\frac{1}{1 + y + yz} =\\\\\frac{yz +y+1}{1 + y + yz} =1[/tex]