Question

Lim x -4 sqrt x+20 - sqrt 12-x x^ 2 +3x-4 =

Answer 1

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Answer 2

Step-by-step explanation:

$= \lim \limits_{x \to - 4} \frac{ \sqrt{x + 20} - \sqrt{12 - x} }{ {x}^{2} + 3x - 4 }$

$= \lim \limits_{x \to - 4} \frac{ \sqrt{x + 20} - \sqrt{12 - x} }{(x + 4)(x - 1)} \times \frac{ \sqrt{x + 20} + \sqrt{12 - x} }{ \sqrt{x + 20} + \sqrt{12 - x } }$

$= \lim \limits_{x \to - 4} \frac{ {( \sqrt{x + 20} )}^{2} - {( \sqrt{12 - x} )}^{2} }{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )}$

$= \lim \limits_{x \to - 4} \frac{x + 20 - 12 + x }{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )}$

$= \lim \limits_{x \to - 4} \frac{2x + 8}{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )}$

$= \lim \limits_{x \to - 4} \frac{2 \cancel{(x + 4)}}{ \cancel{(x + 4)}(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )}$

$= \lim \limits_{x \to - 4} \frac{2}{(x + 1)( \sqrt{x + 20} + \sqrt{12 - x} )}$

$= \frac{2}{( - 4 + 1)( \sqrt{ - 4 + 20} + \sqrt{12 + 4} ) }$

$= \frac{2}{( - 3)( \sqrt{16} + \sqrt{16}) }$

$= \frac{2}{( - 3)(4 + 4)}$

$= \frac{2}{( - 3)(16)}$

$= \frac{1}{( - 3)(8)}$

$= - \frac{1}{24}$