Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.5" was replaced by "(35/10)".

Step  1  :

            7
 Simplify   —
            2

Equation at the end of step  1  :

                       7
  ((4 • (x2)) -  x) -  —
                       2
 Step  2  :

Equation at the end of step  2  :

                 7
  (22x2 -  x) -  —
                 2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

                4x2 - x     (4x2 - x) • 2
     4x2 - x =  ———————  =  —————————————
                   1              2      

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 :

   4x² - x  =   x • (4x - 1) 

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 • (4x-1) • 2 - (7)     8x2 - 2x - 7
 ————————————————————  =  ————————————
          2                    2      

Trying to factor by splitting the middle term

 4.3     Factoring  8x² - 2x - 7 

The first term is,  8x²  its coefficient is  8 .
The middle term is,  -2x  its coefficient is  -2 .
The last term, "the constant", is  -7 

Step-1 : Multiply the coefficient of the first term by the constant   8 • -7 = -56 

Step-2 : Find two factors of  -56  whose sum equals the coefficient of the middle term, which is   -2 .

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

Final result :

  8x2 - 2x - 7
  ————————————
       2