Evaluate the following limit : lim(x→2)(x/(x - 2) - 4/(x^2- 2x))

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 2}\left(\cfrac{\text x}{\text x-2}-\cfrac{4}{\text x^2-2\text x}\right) \)

lim(x→2)(x/(x - 2) - 4/(x²- 2x))

Answer 1

\(=\lim\limits_{\text x \to 2}\left(\cfrac{\text x}{\text x-2}-\cfrac{4}{\text x^2-2\text x}\right) \)

Since a²- b² = (a + b)(a - b)

= 2