Solve and show steps!
(x^2 - x - 12) / (x-4)

x+3

Step-by-step explanation:

           x2 - x - 12

Simplify   ———————————

              x - 4    

Trying to factor by splitting the middle term

1.1     Factoring  x2 - x - 12  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -12  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -12 = -12  

Step-2 : Find two factors of  -12  whose sum equals the coefficient of the middle term, which is   -1 .

     -12    +    1    =    -11  

     -6    +    2    =    -4  

     -4    +    3    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  3  

                    x2 - 4x + 3x - 12

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-4)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-4)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x-4)

            Which is the desired factorization

Canceling Out :

1.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 x + 3

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

n

step-by-step explanation: