Solution - Reducing fractions to their lowest terms

Step  1  :

Equation at the end of step  1  :

   (((3•(x3))-(5•(x2)))-(2•17x24)) 
  (———————————————————————————————•x)-2
                  3               
 Step  2  :

Equation at the end of step  2  :

   (((3•(x3))-5x2)-(2•17x24)) 
  (——————————————————————————•x)-2
               3             
 Step  3  :

Equation at the end of step  3  :

   ((3x3 - 5x2) - (2•17x24))          
  (————————————————————————— • x) -  2
               3                     

Step  4  :

            -34x24 + 3x3 - 5x2 
 Simplify   ——————————————————
                    3         

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -34x²⁴ + 3x³ - 5x²  =   -x² • (34x²² - 3x + 5) 

Equation at the end of step  5  :

   -x2 • (34x22 - 3x + 5)          
  (—————————————————————— • x) -  2
             3                    

Step  6  :

Multiplying exponential expressions :

 6.1    x² multiplied by x¹ = x^{(2 + 1)} = x³

Equation at the end of step  6  :

  -x3 • (34x22 - 3x + 5)     
  —————————————————————— -  2
            3               

Step  7  :

Rewriting the whole as an Equivalent Fraction :

 7.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         2     2 • 3
    2 =  —  =  —————
         1       3  

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 :

 7.2       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:

 -x3 • (34x22-3x+5) - (2 • 3)      -34x25 + 3x4 - 5x3 - 6 
 ————————————————————————————  =  ——————————————————————
              3                             3           

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   -34x²⁵ + 3x⁴ - 5x³ - 6  = 

  -1 • (34x²⁵ - 3x⁴ + 5x³ + 6) 

Checking for a perfect cube :

 8.2    34x²⁵ - 3x⁴ + 5x³ + 6  is not a perfect cube

Trying to factor by pulling out :

 8.3      Factoring:  34x²⁵ - 3x⁴ + 5x³ + 6 

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

Group 1:  5x³ + 6 
Group 2:  34x²⁵ - 3x⁴ 

Pull out from each group separately :

Group 1:   (5x³ + 6) • (1)
Group 2:   (34x²¹ - 3) • (x⁴)

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 :

  +34x25 + 3x4 + 5x3 + 6 
  ——————————————————————
            3