Calculate the limit algebraically.
A)6
B)-2
C)0
D)8
E)10

Question

Calculate the limit algebraically. 
A)6 
B)-2 
C)0 
D)8 
E)10

Quizplus · Accepted Answer

To calculate the limit algebraically, we need to factor and cancel out the common terms if possible. 
Here, we can factor out "x" from the numerator and denominator. 
So, the expression becomes (3x^2 - 3x) / (2x^2 + 4x - 12)
Now, we can further simplify the equation by canceling out the common factor of 3 from the numerator and denominator. 
So, the expression becomes (x^2 - x) / (2x^2 + 4x - 12)
Next, we can factor the denominator by taking out the common factor of 2. 
So, the expression becomes (x^2 - x) / 2(x^2 + 2x - 6)
Now, we can factor the denominator by finding two numbers whose product is -6 and sum is 2. 
The numbers are 3 and -1. 
So, the expression becomes (x^2 - x) / 2(x+3)(x-1)
Now, we can cancel out the common factor of (x-1) from the numerator and denominator. 
So, the expression becomes x / 2(x+3)
Finally, we can substitute x = -6 in the expression to get the limit.
So, the limit of the expression as x approaches -6 is (-6) / 2(-6+3) which is equal to 6. 
Therefore, the best choice is A)6.

Calculate the Limit Algebraically