JEE MainMathematicsModerateLimits, continuity and derivability

$\lim_{x \rightarrow - 1}\mspace{2mu}\left( \frac{1}{1 + x} - \frac{3}{1 + x^{3}} \right)$
is equal to

Show answer and solution

\lim_{x \rightarrow - 1}\mspace{2mu}\left( \frac{1}{1 + x} - \frac{3}{1 + x^{3}} \right) = \lim_{x \rightarrow - 1}\mspace{2mu}\frac{1 + x^{2} - x - 3}{(1 + x)\left( x^{2} - x + 1 \right)}

= \lim_{x \rightarrow - 1}\mspace{2mu}\frac{(x + 1)(x - 2)}{(x + 1)\left( x^{2} - x + 1 \right)} = \frac{- 3}{3} = - 1

Source: Grass-G / M-11 Mathematics Paper-2 1Nov.docx

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