Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.1" was replaced by "(1/10)". 2 more similar replacement(s)

Step  1  :

             1
 Simplify   ——
            10

Equation at the end of step  1  :

   999       1
  {———}2 - (——)2)
   10       10

Step  2  :

 2.1     10 = 2•5 (10)² = (2•5)² = 2² • 5²

Equation at the end of step  2  :

   999        1   
  {———}2 - ———————
   10      (22•52)

Step  3  :

            999
 Simplify   ———
            10 

Equation at the end of step  3  :

   999          1   
  (———)2) -  ———————
   10        (22•52)

Step  4  :

 4.1     999 = 33•37

(999)² = (3³•37)² = 3⁶ • 37²  4.2     10 = 2•5 (10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

  (36•372)       1   
  ———————— -  ———————
  (22•52)     (22•52)

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 (36•372) - (1)     36•372 - 1
 ——————————————  =  ——————————
      100              100    

Final result :

  999 - 1
  ———————
    100