1. If $\frac{x y}{(z+x)(y+z)}+\frac{y z}{(x+y)(z+x)}$ $+\frac{z x}{(y+z)(x+y)}=1$, then the values of $x, y, z$ are ( ).
(A) all zero
(B) only two are zero
(C) only one is zero
(D) all are non-zero
$-1 .(\mathrm{C})$.
The original equation can be rewritten as $x y z=0$, then at least one of $x, y, z$ is zero. If two or three of $x, y, z$ are zero, the denominator in the original equation would be undefined. Therefore, only one of $x, y, z$ is zero.