\(A=\frac{x}{x+y+z}+\frac{y}{x+y+t}+\frac{z}{x+z+t}+\frac{t}{y+z+t}\)
\(A< \frac{x}{x+y}+\frac{y}{x+y}+\frac{z}{z+t}+\frac{t}{z+t}=\frac{x+y}{x+y}+\frac{z+t}{z+t}=2\)
\(A>\frac{x}{x+y+z+t}+\frac{y}{x+y+z+t}+\frac{z}{x+y+z+t}+\frac{t}{x+y+z+t}=\frac{x+y+z+t}{x+y+z+t}=1\)
Suy ra \(1< A< 2\)do đó \(A\)không là số tự nhiên.