Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle\lim_{x \to 1} \: \left ( \frac {2} {x^2-1}-\frac {1}{x-1} \right )$ is gelijk aan	A. − 1
	B.
	C. 0
	D.
	E.

[ 6-6974 - op net sinds 8.3.14-(E)-9.11.2023 ]

Translation in E N G L I S H

$\displaystyle\lim_{x \to 1} \: \left ( \frac {2} {x^2-1}-\frac {1}{x-1} \right )$ is equal to	A. − 1
	B.
	C. 0
	D. ∞
	E. − ∞

Oplossing - Solution

$\\\ displaystyle \lim_{x \to 1}\left (\frac{2}{x^2-1}-\frac{1}{x-1} \right )= \ displaystyle \lim_{x \to 1}\left (\frac{2}{x^2-1}-\frac{x+1}{x^2-1} \right )= \displaystyle \lim_{x \to 1}\left ( \frac{2-x-1}{x^2-1} \right )\\{\color{Green} .}\qquad\qquad\qquad\qquad= \displaystyle \lim_{x \to 1}\left ( \frac{1-x}{(x-1)(x+1)} \right )= \displaystyle \lim_{x \to 1}\left ( \frac{-1}{x+1} \right ) =-\frac12$