Solution - Adding, subtracting and finding the least common multiple

Step  1  :

Equation at the end of step  1  :

  (4x • (52))    54
  ——————————— -  ——
       3         4 

Step  2  :

            54
 Simplify   ——
            4 

Equation at the end of step  2  :

  (4x • (52))    625
  ——————————— -  ———
       3          4 

Step  3  :

Equation at the end of step  3  :

  (4x • 52)    625
  ————————— -  ———
      3         4 

Step  4  :

Equation at the end of step  4  :

  (22•52x)    625
  ———————— -  ———
     3         4 

Step  5  :

            (22•52x)
 Simplify   ————————
               3    

Equation at the end of step  5  :

  100x    625
  ———— -  ———
   3       4 

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       3 

      The right denominator is :       4 

      Least Common Multiple:
      12 

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 = 4

   Right_M = L.C.M / R_Deno = 3

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.      100x • 4
   ——————————————————  =   ————————
         L.C.M                12   

   R. Mult. • R. Num.      625 • 3
   ——————————————————  =   ———————
         L.C.M               12   

Adding fractions that have a common denominator :

 6.4       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:

 100x • 4 - (625 • 3)     400x - 1875
 ————————————————————  =  ———————————
          12                  12     

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   400x - 1875  =   25 • (16x - 75) 

Final result :

  25 • (16x + 75)
  ———————————————
        12