Ta có:$P=\dfrac{x}{x+y+z}+\dfrac{y}{x+y+t}+\dfrac{z}{t+y+z}+\dfrac{z}{x+t+z}$
$<\dfrac{x+t}{x+y+z+t}+\dfrac{y+z}{x+y+z+t}+\dfrac{x+z}{x+t+y+z}+\dfrac{z+y}{x+y+t+z}$
$=\dfrac{2(x+y+z+t)}{x+y+z+t}=2$
Mặt khác:
$P>\dfrac{x}{x+y+z+t}+\dfrac{y}{x+y+z+t}+\dfrac{z}{z+t+y+z}+\dfrac{z}{x+t+z+y}$
$=\dfrac{x+y+z+t}{z+y+z+t}=1$
Suy ra $P$ không thể là số nguyên.