\[ \begin{split} &\lim_{x \to 1}\frac{1-x^2}{\left(1-\sqrt{x}\right)} =\\[16pt] &=\lim_{x \to 1}\frac{(1-x)(1+x)}{\left(1-\sqrt{x}\right)} =\\[16pt] &=\lim_{x \to 1}\frac{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)(1+x)}{\left(1-\sqrt{x}\right)} =\\[16pt] &=\lim_{x \to 1} \left(1+\sqrt{x}\right)(1+x)=\\[16pt] &=2\cdot 2=4 \end{split} \]