a) $$ \displaylines{ \begin{align} \lim_{x\to1}\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}&=\lim_{x\to1}\frac{\sqrt[3]{x}-1}{\sqrt[4]{x}-1}\cdot\frac{\sqrt[3]{x}+1}{\sqrt[3]{x}+1}\ \end{align} }
\displaylines{ \begin{align} \lim_{x\to1}\frac{x^3-1}{x^2-1}&=\lim_{x\to1}\frac{(x-1)(x^2+x+1)}{(x+1)(x-1)}\ &=\lim_{x\to1}\frac{x^2+x+1}{x+1}\ &=\frac{3}{2} \end{align} }
\displaylines{ \begin{align} \lim_{x\to5}\frac{x^2-3x-10}{25-x^2}&=\lim_{x\to5}\frac{(x-5)(x+2)}{(5-x)(5+x)}\ &=\lim_{x\to5}\frac{(x-5)(x+2)}{-(x-5)(5+x)}\ &=\lim_{x\to5}\frac{x+2}{-x-5}\ &=\frac{7}{-10}\ &=\frac{-7}{10} \end{align} }