Solution - Adding, subtracting and finding the least common multiple

Step  1  :

            6a - 9b
 Simplify   ———————
              2a   

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   6a - 9b  =   3 • (2a - 3b) 

Equation at the end of step  2  :

  (4a - 8b)    3 • (2a - 3b)
  ————————— -  —————————————
     2a             2a      

Step  3  :

            4a - 8b
 Simplify   ———————
              2a   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   4a - 8b  =   4 • (a - 2b) 

Equation at the end of step  4  :

  2 • (a - 2b)    3 • (2a - 3b)
  ———————————— -  —————————————
       a               2a      

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       a 

      The right denominator is :       2a 

      Least Common Multiple:
      2a 

Calculating Multipliers :

 5.2    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 = 2

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 5.3      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.      2 • (a-2b) • 2
   ——————————————————  =   ——————————————
         L.C.M                   2a      

   R. Mult. • R. Num.      3 • (2a-3b)
   ——————————————————  =   ———————————
         L.C.M                 2a     

Adding fractions that have a common denominator :

 5.4       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:

 2 • (a-2b) • 2 - (3 • (2a-3b))     b - 2a
 ——————————————————————————————  =  ——————
               2a                     2a  

Final result :

  b - 2a
  ——————
    2a