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Factorization Method Form to Remove Indeterminate Form

Calculate the...

Question

Calculate the following limits.
$lim x \to 1 \frac{x^{2} + 5 x - 6}{x - x^{2}} .$

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Solution

$lim x \to 1 \frac{x^{2} + 5 x - 6}{x - x^{2}}$

$= lim x \to 1 \frac{(x + 6) (x - 1)}{x (1 - x)}$

$= - 7$

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