k,
$x\to -\infty\Rightarrow x<0$
$\lim\limits_{x\to -\infty}\dfrac{(x+1)\sqrt{x^2+3x+2}}{2x^2-4x+5}$
$=\lim\limits_{x\to -\infty}\dfrac{ x\Big(1+\dfrac{1}{x}\Big).(-x)\sqrt{1+\dfrac{3}{x}+\dfrac{2}{x^2}} }{2x^2-4x+5}$
$=\lim\limits_{x\to -\infty}\dfrac{-\Big(1+\dfrac{1}{x}\Big)\sqrt{1+\dfrac{3}{x}+\dfrac{2}{x^2}} }{2-\dfrac{4}{x}+\dfrac{5}{x^2}}$
$=\dfrac{-1.1}{2}$
$=\dfrac{-1}{2}$
