Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

         1       3
  -2 • (—— ÷ 6 - —)
        35       2

Step  2  :

             1
 Simplify   ——
            35

Equation at the end of step  2  :

         1        3
  -2 • (—— ÷ 6 -  —)
        35        2

Step  3  :

          1      
 Divide  ——  by  6
         35      

Equation at the end of step  3  :

         1     3
  -2 • (——— -  —)
        210    2

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       210 

      The right denominator is :       2 

      Least Common Multiple:
      210 

Calculating Multipliers :

 4.2    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 = 1

   Right_M = L.C.M / R_Deno = 105

Making Equivalent Fractions :

 4.3      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.       1 
   ——————————————————  =   ———
         L.C.M             210

   R. Mult. • R. Num.      3 • 105
   ——————————————————  =   ———————
         L.C.M               210  

Adding fractions that have a common denominator :

 4.4       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:

 1 - (3 • 105)     -157
 —————————————  =  ————
      210          105 

Equation at the end of step  4  :

       -157
  -2 • ————
       105 

Step  5  :

Final result :

  314           
  ——— = 2.99048 
  105