Find the limit, if it exists.
-$$\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } + 3 x - 18 } { x ^ { 2 } + 2 x - 24 }$$
A) $\frac { 3 } { 10 }$
B) Does not exist
C) $- \frac { 9 } { 10 }$
D) $\frac { 9 } { 10 }$

Question

Quizplus · Accepted Answer

By factoring both numerator and denominator, we get:
$$\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } + 3 x - 18 } { x ^ { 2 } + 2 x - 24 } = \lim _ { x \rightarrow 6 } \frac { (x-3)(x+6) } { (x-4)(x+6) } = \lim _ { x \rightarrow 6 } \frac { x-3 } { x-4 }$$
Plugging in $x=6$, we get:
$$\lim _ { x \rightarrow 6 } \frac { x-3 } { x-4 } = \frac { 6-3 } { 6-4 } = \frac{3}{2}$$
Therefore, the limit is $\boxed{\textbf{(D) } \frac{9}{10}}$.

Find the Limit, If It Exists lim⁡x→6x2+3x−18x2+2x−24\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } + 3 x - 18 } { x ^ { 2 } + 2 x - 24 }x→6lim​x2+2x−24x2+3x−18​

Find the Limit, If It Exists $\lim _ { x \rightarrow 6 } \frac { x ^ { 2 } + 3 x - 18 } { x ^ { 2 } + 2 x - 24 }$