Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.1" was replaced by "(1/10)". 2 more similar replacement(s)

Step  1  :

             1
 Simplify   ——
            10

Equation at the end of step  1  :

          3            1
  (1 -  (—— • x)) -  (—— • x2)
         10           10

Step  2  :

Equation at the end of step  2  :

          3          x2
  (1 -  (—— • x)) -  ——
         10          10

Step  3  :

             3
 Simplify   ——
            10

Equation at the end of step  3  :

          3          x2
  (1 -  (—— • x)) -  ——
         10          10

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

          1     1 • 10
     1 =  —  =  ——————
          1       10  

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 :

 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:

 10 - (3x)     10 - 3x
 —————————  =  ———————
    10           10   

Equation at the end of step  4  :

  (10 - 3x)    x2
  ————————— -  ——
     10        10

Step  5  :

Adding fractions which have a common denominator :

 5.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (10-3x) - (x2)     -x2 - 3x + 10
 ——————————————  =  —————————————
       10                10      

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -x² - 3x + 10  =   -1 • (x² + 3x - 10) 

Trying to factor by splitting the middle term

 6.2     Factoring  x² + 3x - 10 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +3x  its coefficient is  3 .
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   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  5 
                     x² - 2x + 5x - 10

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

Final result :

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