Answer:
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
  
 STEP 
2
 :
Equation at the end of step
2
:
  
STEP
3
:
            2x3 - x2 - 6x
 Simplify   —————————————
            2x2 - 7x + 6 
STEP
4
:
Pulling out like terms
 4.1     Pull out like factors :
   2x3 - x2 - 6x  =   x • (2x2 - x - 6) 
Trying to factor by splitting the middle term
 4.2     Factoring  2x2 - x - 6 
The first term is,  2x2  its coefficient is  2 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -6 
Step-1 : Multiply the coefficient of the first term by the constant   2 • -6 = -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 
                     2x2 - 4x + 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x-2)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-2)
Step-5 : Add up the four terms of step 4 :
                    (2x+3)  •  (x-2)
             Which is the desired factorization
Trying to factor by splitting the middle term
 4.3     Factoring  2x2-7x+6 
The first term is,  2x2  its coefficient is  2 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  +6 
Step-1 : Multiply the coefficient of the first term by the constant   2 • 6 = 12 
Step-2 : Find two factors of  12  whose sum equals the coefficient of the middle term, which is   -7 .
      -12    +    -1    =    -13	
      -6    +    -2    =    -8	
      -4    +    -3    =    -7    That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -3 
                     2x2 - 4x - 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x-2)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-2)
Step-5 : Add up the four terms of step 4 :
                    (2x-3)  •  (x-2)
             Which is the desired factorization
Canceling Out :
 4.4    Cancel out  (x-2)  which appears on both sides of the fraction line.
Final result :
  x • (2x + 3)
  ————————————
     2x - 3