\(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)}{2x^2+x-3}\)
= \(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)}{(2x+3)( x-1)}\)
= \(\lim\limits_{x \to 1}\frac{(2x-3)(\sqrt x-1)(\sqrt x+1)}{(2x+3)(x-1)(\sqrt x+1)}\)
= \(\lim\limits_{x \to 1}\frac{(2x-3)(x-1)}{(2x+3)(x-1)(\sqrt x+1)}\) [ x ≠ 1]
= \(\lim\limits_{x \to 1}\frac{(2x-3)}{(2x+3)((\sqrt x+1)}\)
= \(\frac{2.1-3}{(2.1+3)(1+1)}\)
= \(\frac{-1}{5.2}\)
= \(-\frac{1}{10}\)