Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "10.1038" was replaced by "(101038/10000)".

Step  1  :

            50519
 Simplify   —————
            5000 

Equation at the end of step  1  :

    50519                              
  ((————— ÷ s41564 -  23) -  1328) -  8
    5000                               

Step  2  :

         50519      
 Divide  —————  by  s41564
         5000       

Equation at the end of step  2  :

     (72•1031)                    
  ((—————————— -  23) -  1328) -  8
    5000s41564                     

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁶⁴  as the denominator :

          23     23 • 5000s41564
    23 =  ——  =  ———————————————
          1        5000s41564   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       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:

 (72•1031) - (23 • 5000s41564)     72•1031 - 115000s41564
 —————————————————————————————  =  ——————————————————————
          5000s41564                     5000s41564      

Equation at the end of step  3  :

   (72•1031 - 115000s41564)             
  (———————————————————————— -  1328) -  8
          5000s41564                    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁶⁴  as the denominator :

            1328     1328 • 5000s41564
    1328 =  ————  =  —————————————————
             1          5000s41564    

Trying to factor as a Difference of Squares :

 4.2      Factoring:  50519 - 115000s⁴¹⁵⁶⁴ 

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 :  50519  is not a square !!

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

Adding fractions that have a common denominator :

 4.3       Adding up the two equivalent fractions

 (50519-115000s41564) - (1328 • 5000s41564)      50519 - 6755000s41564
 ——————————————————————————————————————————  =  —————————————————————
                 5000s41564                          5000s41564      

Equation at the end of step  4  :

  (50519 - 6755000s41564)    
  ——————————————————————— -  8
        5000s41564           

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁵⁶⁴  as the denominator :

         8     8 • 5000s41564
    8 =  —  =  ——————————————
         1       5000s41564  

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   50519 - 6755000s⁴¹⁵⁶⁴  =   7 • (7217 - 965000s⁴¹⁵⁶⁴) 

Adding fractions that have a common denominator :

 6.2       Adding up the two equivalent fractions

 7 • (7217-965000s41564) - (8 • 5000s41564)      50519 - 6795000s41564
 ——————————————————————————————————————————  =  —————————————————————
                 5000s41564                          5000s41564      

Final result :

  50519 - 6795000s41564
  —————————————————————
       5000s41564