Question

Упростите выражение.

$\frac{1}{(x-y)(y-z)} - \frac{1}{(z-y)(z-x)}+\frac{1}{(y-x)(x-z)}$

Answer 1

$\frac{1}{(x-y)(y-z)}-\frac{1}{(z-y)(z-x)}+\frac{1}{(y-x)(x-z)}=\frac{1}{(x-y)(y-z)}-\frac{1}{(y-z)(x-z)}-\frac{1}{(x-y)(x-z)}=\frac{x-z-x+y-y+z}{(x-y)(y-z)(x-z)}=\frac{0}{(x-y)(y-z)(x-z)}=0\\\\Otvet:\boxed{0}$