Simplify and solve (show work please)

5/7b+2/3(b+4/3)-9

87b - 511

 —————————

    63    

Step-by-step explanation:

Step by step solution :

Step  1  :

           4

Simplify   —

           3

Equation at the end of step  1  :

   5     2    4

 ((—•b)+(—•(b+—)))-9

   7     3    3

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  3  as the denominator :

         b     b • 3

    b =  —  =  —————

         1       3  

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 :

2.2       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:

b • 3 + 4     3b + 4

—————————  =  ——————

    3           3  

Equation at the end of step  2  :

   5     2 (3b+4)

 ((—•b)+(—•——————))-9

   7     3   3  

Step  3  :

           2

Simplify   —

           3

Equation at the end of step  3  :

   5          2   (3b + 4)      

 ((— • b) +  (— • ————————)) -  9

   7          3      3          

Step  4  :

Equation at the end of step  4  :

   5         2 • (3b + 4)    

 ((— • b) +  ————————————) -  9

   7              9          

Step  5  :

           5

Simplify   —

           7

Equation at the end of step  5  :

   5         2 • (3b + 4)    

 ((— • b) +  ————————————) -  9

   7              9          

Step  6  :

Calculating the Least Common Multiple :

6.1    Find the Least Common Multiple

     The left denominator is :       7

     The right denominator is :       9

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

7101

3022

Product of all

Prime Factors  7963

     Least Common Multiple:

     63

Calculating Multipliers :

6.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 9

  Right_M = L.C.M / R_Deno = 7

Making Equivalent Fractions :

6.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      5b • 9

  ——————————————————  =   ——————

        L.C.M               63  

  R. Mult. • R. Num.      2 • (3b+4) • 7

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

        L.C.M                   63      

Adding fractions that have a common denominator :

6.4       Adding up the two equivalent fractions

5b • 9 + 2 • (3b+4) • 7     87b + 56

———————————————————————  =  ————————

          63                   63  

Equation at the end of step  6  :

 (87b + 56)    

 —————————— -  9

     63        

Step  7  :

Rewriting the whole as an Equivalent Fraction :

7.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  63  as the denominator :

        9     9 • 63

   9 =  —  =  ——————

        1       63  

Adding fractions that have a common denominator :

7.2       Adding up the two equivalent fractions

(87b+56) - (9 • 63)     87b - 511

———————————————————  =  —————————

        63                 63    

Final result :

 87b - 511

 —————————

    63