Question

6x+3/x^2-4*x^2+7x+6/2x^2+3x+1 please help

Answer 1

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