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                   
  ((— • v2) +  24v) -  5
    2                   

Step  2  :

Equation at the end of step  2  :

   v2            
  (—— +  24v) -  5
   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 :

           24v     24v • 2
    24v =  ———  =  ———————
            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:

 v2 + 24v • 2     v2 + 48v
 ————————————  =  ————————
      2              2    

Equation at the end of step  3  :

  (v2 + 48v)    
  —————————— -  5
      2         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

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

         5     5 • 2
    5 =  —  =  —————
         1       2  

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   v² + 48v  =   v • (v + 48) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 v • (v+48) - (5 • 2)     v2 + 48v - 10
 ————————————————————  =  —————————————
          2                     2      

Trying to factor by splitting the middle term

 5.3     Factoring  v² + 48v - 10 

The first term is,  v²  its coefficient is  1 .
The middle term is,  +48v  its coefficient is  48 .
The last term, "the constant", is  -10 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10 

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   48 .

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

Final result :

  v2 + 48v + 10
  —————————————
        2