Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.5" was replaced by "(5/10)".

Step  1  :

            1
 Simplify   —
            2

Equation at the end of step  1  :

    1                  
  ((— • x2) +  4x) +  9
    2                  

Step  2  :

Equation at the end of step  2  :

   x2           
  (—— +  4x) +  9
   2            

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

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

          4x     4x • 2
    4x =  ——  =  ——————
          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

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:

 x2 + 4x • 2     x2 + 8x
 ———————————  =  ———————
      2             2   

Equation at the end of step  3  :

  (x2 + 8x)    
  ————————— +  9
      2        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

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

         9     9 • 2
    9 =  —  =  —————
         1       2  

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   x² + 8x  =   x • (x + 8) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 x • (x+8) + 9 • 2     x2 + 8x + 18
 —————————————————  =  ————————————
         2                  2      

Trying to factor by splitting the middle term

 5.3     Factoring  x² + 8x + 18 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +8x  its coefficient is  8 .
The last term, "the constant", is  +18 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18 

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   8 .

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

Final result :

  x2 + 8x + 18
  ————————————
       2