Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.5" was replaced by "(45/10)".

Step  1  :

            9
 Simplify   —
            2

Equation at the end of step  1  :

            9          
  ((x2) -  (— • x)) -  9
            2          
 Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

           x2     x2 • 2
     x2 =  ——  =  ——————
           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 :

 2.2       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 • 2 - (9x)     2x2 - 9x
 —————————————  =  ————————
       2              2    

Equation at the end of step  2  :

  (2x2 - 9x)    
  —————————— -  9
      2         

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

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

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x² - 9x  =   x • (2x - 9) 

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 x • (2x-9) - (9 • 2)     2x2 - 9x - 18
 ————————————————————  =  —————————————
          2                     2      

Trying to factor by splitting the middle term

 4.3     Factoring  2x² - 9x - 18 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  -9x  its coefficient is  -9 .
The last term, "the constant", is  -18 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -18 = -36 

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -9 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  3 
                     2x² - 12x + 3x - 18

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (x-6)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-6)
Step-5 : Add up the four terms of step 4 :
                    (2x+3)  •  (x-6)
             Which is the desired factorization

Final result :

  (x - 6) • (2x + 3)
  ——————————————————
          2