If $\frac{x-1}{l}=\frac{y-2}{m}=\frac{z+1}{n}$ is the equation of the line passing through $(1,2,-1)$ and $(-1,0,1)$, then $(l,m,n)$ is:

The direction ratios $(l,m,n)$ of a line passing through $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ are proportional to $(x_2-x_1,y_2-y_1,z_2-z_1)$.Here, $P_1=(1,2,-1)$ and $P_2=(-1,0,1)$.DRs $=(-1-1,0-2,1-(-1))=(-2,-2,2)$.Any set proportional to $(-2,-2,2)$ can be used. Dividing by $-2$:
$$(l,m,n)=(1,1,-1)$$