STEP
1
:
2v - 6
Simplify ——————
v + 2
STEP
2
:
Pulling out like terms
2.1 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
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
STEP
4
:
v-3 2•(v-3)
Divide ————— by ———————
(v+2) (v+2)
4.1 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
——————— ÷ ——————————— = ——————— • ———————————
(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
— = 0.50000
2
