Evaluate the following limit : lim(x→1) (1/(x^2 + x - 2) - x/(x^3 - 1))

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 1}\left(\cfrac{1}{\text x^2+\text x - 2}-\cfrac{\text x}{\text x^3-1}\right) \) 

lim(x→1) (1/(x² + x - 2) - x/(x³ - 1))

Answer 1

\(\lim\limits_{\text x \to 1}\left(\cfrac{1}{\text x^2+\text x - 2}-\cfrac{\text x}{\text x^3-1}\right) \)

Hence,

\(\lim\limits_{\text x \to 1}\left(\cfrac{1}{\text x^2+\text x - 2}-\cfrac{\text x}{\text x^3-1}\right) \) = \(\cfrac{-1}9\)