STEP
1
:
      2v - 6
Simplify  ——————
      v + 2
STEP
2
:
Pulling out like terms
2.1 Â Â Pull out like factors :
 2v - 6  =  2 • (v - 3)
Equation at the end of step
2
:
 (((v2)+v)-12)  2•(v-3)
 ————————————— ÷ ———————
 (((v2)+6v)+8)   v+2 Â
STEP
3
:
      v2 + v - 12
Simplify  ———————————
      v2 + 6v + 8
Trying to factor by splitting the middle term
3.1   Factoring  v2 + v - 12
The first term is,  v2  its coefficient is  1 .
The middle term is,  +v  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
   -3   +   4   =   1   That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  4
          v2 - 3v + 4v - 12
Step-4 : Add up the first 2 terms, pulling out like factors :
          v • (v-3)
       Add up the last 2 terms, pulling out common factors :
          4 • (v-3)
Step-5 : Add up the four terms of step 4 :
          (v+4)  •  (v-3)
      Which is the desired factorization
Trying to factor by splitting the middle term
3.2   Factoring  v2+6v+8
The first term is,  v2  its coefficient is  1 .
The middle term is,  +6v  its coefficient is  6 .
The last term, "the constant", is  +8
Step-1 : Multiply the coefficient of the first term by the constant  1 • 8 = 8
Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is  6 .
   -8   +   -1   =   -9
   -4   +   -2   =   -6
   -2   +   -4   =   -6
   -1   +   -8   =   -9
   1   +   8   =   9
   2   +   4   =   6   That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  4
          v2 + 2v + 4v + 8
Step-4 : Add up the first 2 terms, pulling out like factors :
          v • (v+2)
       Add up the last 2 terms, pulling out common factors :
          4 • (v+2)
Step-5 : Add up the four terms of step 4 :
          (v+4)  •  (v+2)
      Which is the desired factorization
Canceling Out :
3.3   Cancel out  (v+4)  which appears on both sides of the fraction line.
Equation at the end of step
3
:
 (v - 3)  2 • (v - 3)
 ——————— ÷ ———————————
 v + 2    v + 2 Â
STEP
4
:
     v-3    2•(v-3)
Divide  —————  by  ———————
    (v+2)    (v+2)
4.1 Â Â Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
v - 3    2 • (v - 3)     v - 3     v + 2 Â
———————  ÷  ———————————  =  ———————  •  ———————————
(v + 2)    (v + 2)     (v + 2)   2 • (v - 3)
Canceling Out :
4.2   Cancel out  (v - 3)  which appears on both sides of the fraction line.
Canceling Out :
4.3   Cancel out  (v + 2)  which appears on both sides of the fraction line.
Final result :
 1     Â
 — = 0.50000
 2     Â