Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Please show all your work.

[(x^2 -3x +2)/(x^2 -5x +4)] - [(x^2 + 10x + 24)/(x^2 + 8x + 12)]

Thank you


Sagot :

Answer:

x-8/x-6

Step-by-step explanation:

Step by Step Solution

More Icon

STEP

1

:

              8x - 32  

Simplify   —————————————

           x2 - 10x + 24

STEP

2

:

Pulling out like terms

2.1     Pull out like factors :

  8x - 32  =   8 • (x - 4)

Trying to factor by splitting the middle term

2.2     Factoring  x2 - 10x + 24

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +24

Step-1 : Multiply the coefficient of the first term by the constant   1 • 24 = 24

Step-2 : Find two factors of  24  whose sum equals the coefficient of the middle term, which is   -10 .

     -24    +    -1    =    -25

     -12    +    -2    =    -14

     -8    +    -3    =    -11

     -6    +    -4    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -4

                    x2 - 6x - 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x-4)  •  (x-6)

            Which is the desired factorization

Canceling Out :

2.3    Cancel out  (x-4)  which appears on both sides of the fraction line.

Equation at the end of step

2

:

    ((x2)-4x)     8

 ———————————————-———

 (((x2)-10x)+24) x-6

STEP

3

:

              x2 - 4x  

Simplify   —————————————

           x2 - 10x + 24

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  x2 - 4x  =   x • (x - 4)

Trying to factor by splitting the middle term

4.2     Factoring  x2 - 10x + 24

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +24

Step-1 : Multiply the coefficient of the first term by the constant   1 • 24 = 24

Step-2 : Find two factors of  24  whose sum equals the coefficient of the middle term, which is   -10 .

     -24    +    -1    =    -25

     -12    +    -2    =    -14

     -8    +    -3    =    -11

     -6    +    -4    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -4

                    x2 - 6x - 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x-4)  •  (x-6)

            Which is the desired factorization

Canceling Out :

4.3    Cancel out  (x-4)  which appears on both sides of the fraction line.

Equation at the end of step

4

:

   x        8  

 ————— -  —————

 x - 6    x - 6

STEP

5

:

Adding fractions which have a common denominator :

5.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (8)     x - 8

———————  =  —————

  x-6       x - 6

Final result :

 x - 8

 —————

 x - 6

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.