Solution - Reducing fractions to their lowest terms

Step  1  :

             x
 Simplify   ——
            x2

Dividing exponential expressions :

 1.1    x¹ divided by x² = x^{(1 - 2)} = x^(-1) = ¹/_x¹ = ¹/_x

Equation at the end of step  1  :

       1     
  (4 • —) -  4
       x     

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

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

         4     4 • x
    4 =  —  =  —————
         1       x  

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:

 4 - (4 • x)     4 - 4x
 ———————————  =  ——————
      x            x   

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4 - 4x  =   -4 • (x - 1) 

Final result :

  +4 • (x + 1)
  ————————————
       x