Could someone please check my work

Determine The following limit lim x 2- 1 x - 1+ 1x-11 x 8 - 1 = (x-1) (x+ 1 ) = (x-1) (x+1 ) 1x- 1/ 1x-1 1 1x-'1 = ( 1 - x ) ( - x- 1 ) 1-X = - X- 1 Thus, 2 _1 lim X 1 x - 11 = lim / - x- 1) = -1-1 =-2 x - 1+