In this paper we give the proof of one generalization of the interesting algebraic inequality (1) in [2] \[ \frac{a^n}x+\frac{b^n}y+\frac{c^n}z\geq\frac{(a+b+c)^n}{3^{n-2}(x+y+z)}, \] where $a,b,c,x,y,z,n$ be the positive real numbers and $n\geq2$.