Find the domain of the function

first,
log 0.3{ (x² - 1) / x² - 3x + 2} >0

because we need to find it's square root.

So,
(x² - 1) / (x² - 3x + 2) < 1 (This to me is the important step.) because log(0.3)<0 ... ask again if you dont understand. I will answer again.

now, this remains a simple question of algebra

(x² - 1) / (x² - 3x + 2) - 1 < 0
implies (x²-1-x²+3x-2)/(x² - 3x + 2) < 0
(3x-3)/(x-1)(x-2) < 0
so (x-1)/(x-1)(x-2)<0
at x=1 function is undefined.
otherwise we need x-2<0
so x<2
is the solution. (but we have to exclude point x=1 where the given function is undefined.

So soln is (-∞,1) U (1,2)