limx→111-x-31-x3 is equal

For $x \neq 1, f (x) = \frac{1}{1 - x} - \frac{3}{1 - x^{3}}$

$= \frac{1}{(1 - x)} [1 - \frac{3}{1 + x + x^{2}}]$

$= \frac{1}{(1 - x)} \cdot \frac{x^{2} + x - 2}{(1 + x + x^{2})} = \frac{(x + 2) (x - 1)}{(1 - x) (1 + x + x^{2})}$

$= - \frac{x + 2}{1 + x + x^{2}}$

$so \lim_{x \to 1} f (x) = - \lim_{x \to 1} \frac{x + 2}{1 + x + x^{2}} = - 1$

$\lim_{x \to 1} (\frac{1}{1 - x} - \frac{3}{1 - x^{3}})$ is equal