Find the limit, if it exists.
-$$\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 8 x - 9 } { x ^ { 2 } - 1 }$$
A) Does not exist
B) 5
C) 0
D) - 4

Question

Quizplus · Accepted Answer

Factor both the numerator and denominator first: 
$$\frac { x ^ { 2 } + 8 x - 9 } { x ^ { 2 } - 1 } = \frac {(x-1)(x+9)}{(x-1)(x+1)}$$
Now cancel out the common factor: 
$$\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 8 x - 9 } { x ^ { 2 } - 1 } = \lim _ { x \rightarrow 1 } \frac {(x+9)}{(x+1)}=5$$ 
Therefore, the limit is 5.

Find the Limit, If It Exists lim⁡x→1x2+8x−9x2−1\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 8 x - 9 } { x ^ { 2 } - 1 }x→1lim​x2−1x2+8x−9​

Find the Limit, If It Exists $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 8 x - 9 } { x ^ { 2 } - 1 }$