Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): Dot was discarded near "j.s".

(2): "3.3" was replaced by "(33/10)". 2 more similar replacement(s)

Step  1  :

            33
 Simplify   ——
            10

Equation at the end of step  1  :

            39             33
  ((njsa • ——— ÷ 6) • a) - ——
           100             10

Step  2  :

             39
 Simplify   ———
            100

Equation at the end of step  2  :

            39              33
  ((njsa • ——— ÷ 6) • a) -  ——
           100              10

Step  3  :

          39      
 Divide  ———  by  6
         100      

Equation at the end of step  3  :

            13          33
  ((njsa • ———) • a) -  ——
           200          10
 Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       200 

      The right denominator is :       10 

      Least Common Multiple:
      200 

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 = 20

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.      13njsa2
   ——————————————————  =   ———————
         L.C.M               200  

   R. Mult. • R. Num.      33 • 20
   ——————————————————  =   ———————
         L.C.M               200  

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:

 13njsa2 - (33 • 20)     13njsa2 - 660
 ———————————————————  =  —————————————
         200                  200     

Trying to factor as a Difference of Squares :

 4.5      Factoring:  13njsa² - 660 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  13  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Final result :

  13njsa2 - 660
  —————————————
       200