Answer 1

\(A=\frac{x+y-y}{x+y}+\frac{y+z-z}{y+z}+\frac{z+x-x}{x+z}\)

\(A=3-\left(\frac{x}{x+z}+\frac{y}{x+y}+\frac{z}{y+z}\right)\)

Mà : \(\frac{x}{x+z}>\frac{x}{x+y+z};\frac{y}{y+z}>\frac{y}{x+y+z};\frac{z}{x+z}>\frac{z}{x+y+z}\)

\(\Rightarrow A< 2\left(1\right)\)

Mặt khác : \(A=\frac{x}{x+y}+\frac{y}{y+z}+\frac{z}{x+z}\)

Mà : \(\frac{x}{x+y}>\frac{x}{x+y+z};\frac{y}{y+z}>\frac{y}{x+y+z};\frac{z}{x+z}>\frac{z}{x+y+z}\)

\(\Rightarrow A>1\left(2\right)\)

Từ \(\left(1\right)\left(2\right)\Rightarrow1< A< 2\Rightarrow\notin\)Số nguyên