Solution - Reducing fractions to their lowest terms

Step  1  :

            y3
 Simplify   ——
            4 

Equation at the end of step  1  :

   y3         
  (—— • x) -  4
   4          

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         4     4 • 4
    4 =  —  =  —————
         1       4  

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 :

 2.2       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:

 y3x - (4 • 4)     y3x - 16
 —————————————  =  ————————
       4              4    

Trying to factor as a Difference of Cubes:

 2.3      Factoring:  y³x - 16 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  16  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  y3x - 16
  ————————
     4