Answer:

STEP

1

:

             10xy  

Simplify   ———————

           8y + 3x

Equation at the end of step

1

:

                                   10xy  

 ((2 • (x + y)) • (8x + 24y)) +  ———————

                                 3x + 8y

STEP

2

:

Equation at the end of step 2

                                 10xy  

 (2 • (x + y) • (8x + 24y)) +  ———————

                               3x + 8y

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  8x + 24y  =   8 • (x + 3y)  

Equation at the end of step

4

:

                              10xy  

 16 • (x + y) • (x + 3y) +  ———————

                            3x + 8y

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  (3x+8y)  as the denominator :

                               16 • (x + y) • (x + 3y)     16 • (x + y) • (x + 3y) • (3x + 8y)

    16 • (x + y) • (x + 3y) =  ———————————————————————  =  ———————————————————————————————————

                                          1                             (3x + 8y)              

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

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

16 • (x+y) • (x+3y) • (3x+8y) + 10xy     48x3 + 320x2y + 656xy2 + 10xy + 384y3  

————————————————————————————————————  =  —————————————————————————————————————

            1 • (3x+8y)                              1 • (3x + 8y)            

STEP

6

:

Pulling out like terms :

6.1     Pull out like factors :

  48x3 + 320x2y + 656xy2 + 10xy + 384y3  =  

 2 • (24x3 + 160x2y + 328xy2 + 5xy + 192y3)  

Final result :

 2 • (24x3 + 160x2y + 328xy2 + 5xy + 192y3)  

 ——————————————————————————————————————————

                  3x + 8y                  

Step-by-step explanation:

Hope it helps :)

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