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6v +8 =8 +6v
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1 Answer

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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

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