Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.25" was replaced by "(425/100)".

Step  1  :

            17
 Simplify   ——
            4 

Equation at the end of step  1  :

                         17
  ((2 • (x2)) -  13x) +  ——
                         4 
 Step  2  :

Equation at the end of step  2  :

                  17
  (2x2 -  13x) +  ——
                  4 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

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

                  2x2 - 13x     (2x2 - 13x) • 4
     2x2 - 13x =  —————————  =  ———————————————
                      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

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x² - 13x  =   x • (2x - 13) 

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:

 x • (2x-13) • 4 + 17     8x2 - 52x + 17
 ————————————————————  =  ——————————————
          4                     4       

Trying to factor by splitting the middle term

 4.3     Factoring  8x² - 52x + 17 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  -52x  its coefficient is  -52 .
The last term, "the constant", is  +17 

Step-1 : Multiply the coefficient of the first term by the constant   8 • 17 = 136 

Step-2 : Find two factors of  136  whose sum equals the coefficient of the middle term, which is   -52 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  8x2 - 52x + 17
  ——————————————
        4