Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

            1
 Simplify   —
            1

Equation at the end of step  1  :

            52          
  ((m2) -  (—— • m)) +  1
            10          

Step  2  :

            26
 Simplify   ——
            5 

Equation at the end of step  2  :

            26          
  ((m2) -  (—— • m)) +  1
            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 :

           m2     m2 • 5
     m2 =  ——  =  ——————
           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

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:

 m2 • 5 - (26m)     5m2 - 26m
 ——————————————  =  —————————
       5                5    

Equation at the end of step  3  :

  (5m2 - 26m)    
  ——————————— +  1
       5         

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Adding a whole to a fraction

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

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

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5m² - 26m  =   m • (5m - 26) 

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 m • (5m-26) + 5     5m2 - 26m + 5
 ———————————————  =  —————————————
        5                  5      

Trying to factor by splitting the middle term

 5.3     Factoring  5m² - 26m + 5 

The first term is,  5m²  its coefficient is  5 .
The middle term is,  -26m  its coefficient is  -26 .
The last term, "the constant", is  +5 

Step-1 : Multiply the coefficient of the first term by the constant   5 • 5 = 25 

Step-2 : Find two factors of  25  whose sum equals the coefficient of the middle term, which is   -26 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -25  and  -1 
                     5m² - 25m - 1m - 5

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

Final result :

  (m - 5) • (5m - 1)
  ——————————————————
          5