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$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$
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$-\frac{1}{10}$
$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}$
$\begin{aligned} & =\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{(2 x+3)(x-1)} \times \frac{(\sqrt{x}+1)}{(\sqrt{x}+1)} \\ & =\lim _{x \rightarrow 1} \frac{(2 x-3)(x-1)}{(2 x+3)(x-1)(\sqrt{x}+1)} \\ & =\lim _{x \rightarrow 1} \frac{(2 x-3)}{(2 x+3)(\sqrt{x}+1)}=\frac{-1}{5(2)}=\frac{-1}{10} .\end{aligned}$
$\begin{aligned} & =\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{(2 x+3)(x-1)} \times \frac{(\sqrt{x}+1)}{(\sqrt{x}+1)} \\ & =\lim _{x \rightarrow 1} \frac{(2 x-3)(x-1)}{(2 x+3)(x-1)(\sqrt{x}+1)} \\ & =\lim _{x \rightarrow 1} \frac{(2 x-3)}{(2 x+3)(\sqrt{x}+1)}=\frac{-1}{5(2)}=\frac{-1}{10} .\end{aligned}$
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