Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.04" was replaced by "(04/100)".

Step  1  :

             1
 Simplify   ——
            25

Equation at the end of step  1  :

          1
  -4 +  (—— • k2)
         25

Step  2  :

Equation at the end of step  2  :

        k2
  -4 +  ——
        25

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  25  as the denominator :

           -4     -4 • 25
     -4 =  ——  =  ———————
           1        25   

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:

 -4 • 25 + k2     k2 - 100
 ————————————  =  ————————
      25             25   

Trying to factor as a Difference of Squares :

 3.3      Factoring:  k² - 100 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 100 is the square of 10
Check :  k²  is the square of  k¹ 

Factorization is :       (k + 10)  •  (k - 10) 

Final result :

  (k + 10) • (k - 10)
  ———————————————————
          25