Solution - Reducing fractions to their lowest terms

Step  1  :

            6
 Simplify   —
            y

Equation at the end of step  1  :

           (y4)      6
  ((((y24)•————)-4y)-—)-2
           (y2)      y
 Step  2  :
            y4
 Simplify   ——
            y2

Dividing exponential expressions :

 2.1    y⁴ divided by y² = y^{(4 - 2)} = y²

Equation at the end of step  2  :

                           6     
  ((((y24) • y2) -  4y) -  —) -  2
                           y     

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

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

                 y26 - 4y     (y26 - 4y) • y
     y26 - 4y =  ————————  =  ——————————————
                    1               y       

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

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   y²⁶ - 4y  =   y • (y²⁵ - 4) 

Adding fractions that have a common denominator :

 4.2       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:

 y • (y25-4) • y - (6)     y27 - 4y2 - 6 
 —————————————————————  =  —————————————
           y                     y      

Equation at the end of step  4  :

  (y27 - 4y2 - 6)     
  ——————————————— -  2
         y           

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

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

         2     2 • y
    2 =  —  =  —————
         1       y  

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 (y27-4y2-6) - (2 • y)      y27 - 4y2 - 2y - 6 
 —————————————————————  =  ——————————————————
           y                       y         

Checking for a perfect cube :

 5.3    y²⁷ - 4y² - 2y - 6  is not a perfect cube

Trying to factor by pulling out :

 5.4      Factoring:  y²⁷ - 4y² - 2y - 6 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -2y - 6 
Group 2:  -4y² + y²⁷ 

Pull out from each group separately :

Group 1:   (y + 3) • (-2)
Group 2:   (y²⁵ - 4) • (y²)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Final result :

  y27 + 4y2 + 2y + 6 
  ——————————————————
          y