87b - 511
 —————————
  63  Â
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 Â Adding a fraction to a whole
Rewrite the whole as a fraction using  3  as the denominator :
     b   b • 3
  b =  —  =  —————
     1    3 Â
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 Â Â Â 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 Â
Equation at the end of step  2  :
  5   2 (3b+4)
 ((—•b)+(—•——————))-9
  7   3  3 Â
Step  3  :
      2
Simplify  —
      3
Equation at the end of step  3  :
  5      2  (3b + 4)   Â
 ((— • b) +  (— • ————————)) -  9
  7      3    3     Â
Step  4  :
Equation at the end of step  4  :
  5     2 • (3b + 4)  Â
 ((— • b) +  ————————————) -  9
  7        9     Â
Step  5  :
      5
Simplify  —
      7
Equation at the end of step  5  :
  5     2 • (3b + 4)  Â
 ((— • b) +  ————————————) -  9
  7        9     Â
Step  6  :
Calculating the Least Common Multiple :
6.1 Â Â 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 Â Â 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 Â Â Â 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 Â
 R. Mult. • R. Num.    2 • (3b+4) • 7
 ——————————————————  =  ——————————————
    L.C.M          63   Â
Adding fractions that have a common denominator :
6.4 Â Â Â Adding up the two equivalent fractions
5b • 9 + 2 • (3b+4) • 7   87b + 56
———————————————————————  =  ————————
     63          63 Â
Equation at the end of step  6  :
 (87b + 56)  Â
 —————————— -  9
   63    Â
Step  7  :
Rewriting the whole as an Equivalent Fraction :
7.1 Â Subtracting a whole from a fraction
Rewrite the whole as a fraction using  63  as the denominator :
    9   9 • 63
  9 =  —  =  ——————
    1    63 Â
Adding fractions that have a common denominator :
7.2 Â Â Â Adding up the two equivalent fractions
(87b+56) - (9 • 63)   87b - 511
———————————————————  =  —————————
    63         63  Â
Final result :
 87b - 511
 —————————
  63  Â