$\lim \limits_{x\to 2} \bigg (\dfrac{\sqrt{x-1}-1}{\sqrt{2x}-2} +\dfrac{x^4-3x^3+x^2+4}{\sqrt{2x}-2} \bigg )$
$=\lim \limits_{x\to 2} \bigg (\dfrac{(x-2)(\sqrt{2x}+2)}{2(x-2)(\sqrt{x-1}+1)} +\dfrac{(x-2)^2(x^2+x+1)(\sqrt{2x}+2)}{2(x-2)} \bigg )$
$=\lim \limits_{x\to 2} \bigg (\dfrac{\sqrt{2x}+2}{2(\sqrt{x-1}+1)} +\dfrac{(x-2)(x^2+x+1)(\sqrt{2x}+2)}{2} \bigg )=1$