$\dfrac{m-n}{x(y-z)} = \dfrac{n-p}{y(z-x)} = \dfrac{p-m}{z(x-y)}$
$\textrm{ta có: xyz khác 0}$
$⇒ \dfrac{x(m+n)}{xyz}=\dfrac{y(n+p)}{xyz}=\dfrac{z(p+m)}{xyz}$
$⇒ \dfrac{m+n}{yz} = \dfrac{n+p}{xz} = \dfrac{p+m}{xy}$
$⇒ \dfrac{(p+m)-(n+p)}{xy-xz} = \dfrac{(m+n)-(p+m)}{yz-xy} = \dfrac{(n+p)-(m+n)}{xz-yz}$
$⇒ \dfrac{m-n}{x(y-z)} = \dfrac{n-p}{y(z-x)} = \dfrac{p-m}{z(x-y)}$