`lim_(x->1) (sqrt(2 x - 1) - sqrt(x))/(1 - root3(2 - x))`
`=lim_(x->1) ((sqrt(2 x - 1) - sqrt(x)) (sqrt(x) + sqrt(2 x - 1)))/((1 - \root3(2-x)) (sqrt(x) + sqrt(2 x - 1)))`
`=lim_(x->1)(1-x)/((root3(2-x) - 1) (sqrt(x) + sqrt(2 x - 1)))`
`=(lim_(x->1) 1/(sqrt(x) + sqrt(2 x - 1))) (lim_(x->1) (1-x)/(root3(2-x) - 1))`
`=1/2(lim_(x->1) (1-x)/(root3(2-x) - 1))`
`=(lim_(x->1)(1 + root3(2-x) + root3(2-x)^2))/2`
`=3/2`