Solution - Reducing fractions to their lowest terms

Step  1  :

             d
 Simplify   ——
            dx

Canceling Out :

 1.1    Canceling out d as it appears on both sides of the fraction line

Equation at the end of step  1  :

   1         
  (— • 1) +  3
   x         

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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

         3     3 • x
    3 =  —  =  —————
         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:

 1 + 3 • x     3x + 1
 —————————  =  ——————
     x           x   

Final result :

  3x + 1
  ——————
    x