t: $ \lim _ { x \
ightarrow - 5 } \frac { \sqrt { x + 14 } - 8 } { - 2 x - 2 } $

Question

Accepted Answer

# Explanation:
## Step1: Rationalize the numerator
Multiply the numerator and denominator by the conjugate of the numerator $\sqrt{x + 14}+8$
$$
\begin{align*}
&\lim_{x
ightarrow - 5}\frac{\sqrt{x + 14}-8}{-2x - 2}\times\frac{\sqrt{x + 14}+8}{\sqrt{x + 14}+8}\
=&\lim_{x
ightarrow - 5}\frac{(x + 14)-64}{(-2x - 2)(\sqrt{x + 14}+8)}\
=&\lim_{x
ightarrow - 5}\frac{x - 50}{(-2x - 2)(\sqrt{x + 14}+8)}
\end{align*}
$$
## Step2: Substitute $x=-5$
Substitute $x =-5$ into the expression $\frac{x - 50}{(-2x - 2)(\sqrt{x + 14}+8)}$
$$
\begin{align*}
&\frac{-5-50}{(-2\times(-5)-2)(\sqrt{-5 + 14}+8)}\
=&\frac{-55}{(10 - 2)(3 + 8)}\
=&\frac{-55}{8\times11}\
=&-\frac{5}{8}
\end{align*}
$$

# Answer:
$-\frac{5}{8}$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the numerator

Step2: Substitute \(x=-5\)

Answer: