Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.4" was replaced by "(4/10)".

Step  1  :

            2
 Simplify   —
            5

Equation at the end of step  1  :

                         2
  ((10 • (x2)) +  3x) -  —
                         5
 Step  2  :

Equation at the end of step  2  :

                     2
  ((2•5x2) +  3x) -  —
                     5

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

                  10x2 + 3x     (10x2 + 3x) • 5
     10x2 + 3x =  —————————  =  ———————————————
                      1                5       

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 :

   10x² + 3x  =   x • (10x + 3) 

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 • (10x+3) • 5 - (2)     50x2 + 15x - 2
 —————————————————————  =  ——————————————
           5                     5       

Trying to factor by splitting the middle term

 4.3     Factoring  50x² + 15x - 2 

The first term is,  50x²  its coefficient is  50 .
The middle term is,  +15x  its coefficient is  15 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   50 • -2 = -100 

Step-2 : Find two factors of  -100  whose sum equals the coefficient of the middle term, which is   15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  20 
                     50x² - 5x + 20x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    5x • (10x-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (10x-1)
Step-5 : Add up the four terms of step 4 :
                    (5x+2)  •  (10x-1)
             Which is the desired factorization

Final result :

  (10x + 1) • (5x + 2)
  ————————————————————
           5