Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.05" was replaced by "(805/100)". 2 more similar replacement(s)

Step  1  :

            161
 Simplify   ———
            20 

Equation at the end of step  1  :

         106          161
  (0 -  (——— • x)) -  ———
         10           20 

Step  2  :

            53
 Simplify   ——
            5 

Equation at the end of step  2  :

         53          161
  (0 -  (—— • x)) -  ———
         5           20 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       20 

      Least Common Multiple:
      20 

Calculating Multipliers :

 3.2    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 = 1

Making Equivalent Fractions :

 3.3      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.      -53x • 4
   ——————————————————  =   ————————
         L.C.M                20   

   R. Mult. • R. Num.      161
   ——————————————————  =   ———
         L.C.M             20 

Adding fractions that have a common denominator :

 3.4       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:

 -53x • 4 - (161)     -212x - 161
 ————————————————  =  ———————————
        20                20     

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -212x - 161  =   -1 • (212x + 161) 

Final result :

  +212x + 161
  ———————————
      20