Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.25" was replaced by "(25/100)".

Step  1  :

            1
 Simplify   —
            4

Equation at the end of step  1  :

                  1
  ((x2) +  5x) -  —
                  4

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

                x2 + 5x     (x2 + 5x) • 4
     x2 + 5x =  ———————  =  —————————————
                   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  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   x² + 5x  =   x • (x + 5) 

Adding fractions that have a common denominator :

 3.2       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 • (x+5) • 4 - (1)     4x2 + 20x - 1
 ———————————————————  =  —————————————
          4                    4      

Trying to factor by splitting the middle term

 3.3     Factoring  4x² + 20x - 1 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  +20x  its coefficient is  20 .
The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -1 = -4 

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   20 .

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

Final result :

  4x2 + 20x + 1
  —————————————
        4