Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.13" was replaced by "(13/100)". 4 more similar replacement(s)

Step  1  :

             13
 Simplify   ———
            100

Equation at the end of step  1  :

     95     4      99     13
  ((———•x)-———)-((———•x)-———)
    100    100    100    100

Step  2  :

             99
 Simplify   ———
            100

Equation at the end of step  2  :

     95     4      99     13
  ((———•x)-———)-((———•x)-———)
    100    100    100    100

Step  3  :

Adding fractions which have a common denominator :

 3.1       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:

 99x - (13)     99x - 13
 ——————————  =  ————————
    100           100   

Equation at the end of step  3  :

     95          4      (99x - 13)
  ((——— • x) -  ———) -  ——————————
    100         100        100    

Step  4  :

             1
 Simplify   ——
            25

Equation at the end of step  4  :

     95          1     (99x - 13)
  ((——— • x) -  ——) -  ——————————
    100         25        100    

Step  5  :

            19
 Simplify   ——
            20

Equation at the end of step  5  :

    19          1     (99x - 13)
  ((—— • x) -  ——) -  ——————————
    20         25        100    

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       20 

      The right denominator is :       25 

      Least Common Multiple:
      100 

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 = 5

   Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      19x • 5
   ——————————————————  =   ———————
         L.C.M               100  

   R. Mult. • R. Num.       4 
   ——————————————————  =   ———
         L.C.M             100

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:

 19x • 5 - (4)     95x - 4
 —————————————  =  ———————
      100            100  

Equation at the end of step  6  :

  (95x - 4)    (99x - 13)
  ————————— -  ——————————
     100          100    

Step  7  :

Adding fractions which have a common denominator :

 7.1       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:

 (95x-4) - ((99x-13))     9 - 4x
 ————————————————————  =  ——————
         100               100  

Final result :

  9 - 4x
  ——————
   100