Đáp án: $1$

Giải thích các bước giải:

Ta có:

$\dfrac{2025x}{xy+2025x+2025}+\dfrac{y}{yz+y+2025}+\dfrac{z}{xz+z+1}$

$=\dfrac{2025xz}{xyz+2025xz+2025z}+\dfrac{xzy}{xzyz+xzy+2025xz}+\dfrac{z}{xz+z+1}$

$=\dfrac{2025xz}{2025+2025xz+2025z}+\dfrac{2025}{2025z+2025+2025xz}+\dfrac{z}{xz+z+1}$

$=\dfrac{xz}{1+xz+z}+\dfrac{1}{z+1+xz}+\dfrac{z}{xz+z+1}$

$=\dfrac{xz+1+z}{xz+z+1}$

$=1$