## Related questions with answers

Question

Find $\lim _{x \rightarrow 1} \dfrac{x^2+2 x-3}{x^2-1}$, if it exists.

Solution

VerifiedStep 1

1 of 2$\textbf{Using roperties of limits}$

$\begin{align*} \lim\limits_{x\to 1}\dfrac{\overbrace{x^2+2x-3}^{{\color{#c34632}Factor}}}{\underbrace{x^2-1}_{{\color{#c34632}Factor}}}&=\lim\limits_{x\to 1}\left\{\dfrac{(x-1)(x+3)}{(x-1)(x+1)}\right\}\\\\ &=\lim\limits_{x\to 1}\left\{\dfrac{x+3}{x+1}\right\}\\\\ &=\left\{\dfrac{1+3}{1+1}\right\}\\\\ &=\dfrac42\\\\ &=\color{#19804f}\boxed{\color{#4257b2}2} \end{align*}$

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