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                               
  ((————— ÷ s41467 -  23) -  41105) -  z
    5000                                

Step  2  :

         50519      
 Divide  —————  by  s41467
         5000       

Equation at the end of step  2  :

     (72•1031)                     
  ((—————————— -  23) -  41105) -  z
    5000s41467                      

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁴⁶⁷  as the denominator :

          23     23 • 5000s41467
    23 =  ——  =  ———————————————
          1        5000s41467   

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 • 5000s41467)     72•1031 - 115000s41467
 —————————————————————————————  =  ——————————————————————
          5000s41467                     5000s41467      

Equation at the end of step  3  :

   (72•1031 - 115000s41467)              
  (———————————————————————— -  41105) -  z
          5000s41467                     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁴⁶⁷  as the denominator :

             41105     41105 • 5000s41467
    41105 =  —————  =  ——————————————————
               1           5000s41467    

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 (50519-115000s41467) - (41105 • 5000s41467)      50519 - 205640000s41467
 ———————————————————————————————————————————  =  ———————————————————————
                 5000s41467                            5000s41467       

Equation at the end of step  4  :

  (50519 - 205640000s41467)    
  ————————————————————————— -  z
         5000s41467            

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5000s⁴¹⁴⁶⁷  as the denominator :

         z     z • 5000s41467
    z =  —  =  ——————————————
         1       5000s41467  

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 (50519-205640000s41467) - (z • 5000s41467)      50519 - 5000s41467z - 205640000s41467 
 ——————————————————————————————————————————  =  —————————————————————————————————————
                 5000s41467                                  5000s41467              

Trying to factor a multi variable polynomial :

 5.3    Factoring    50519 - 5000s⁴¹⁴⁶⁷z - 205640000s⁴¹⁴⁶⁷ 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

  50519 + 5000s41467z + 205640000s41467 
  —————————————————————————————————————
               5000s41467