\(\lim\limits_{x\rightarrow1^-}\dfrac{\sqrt{1-x}+x-1}{\sqrt{x^2-x^3}}\)
\(=\lim\limits_{x\rightarrow1^-}\dfrac{\sqrt{1-x}-\left(\sqrt{1-x}\right)^2}{x\cdot\sqrt{1-x}}\)
\(=\lim\limits_{x\rightarrow1^-}\dfrac{1-\sqrt{1-x}}{x}\)
\(=\dfrac{1-\sqrt{1-1}}{1}=1\)