5/x-1/x+3
2/x-3+1/x
Simply

    37 - 3x

 ———————

         x      

Step-by-step explanation:

Step  1  :

                 1

Simplify   —

                  x

Equation at the end of step  1  :

    5 1  32     1

 (((—-—)+——)-3)+—

    x x  x      x

Step  2  :

           32

Simplify   ——

           x

Equation at the end of step  2  :

    5 1  32     1

 (((—-—)+——)-3)+—

    x x  x      x

Step  3  :

           1

Simplify   —

           x

Equation at the end of step  3  :

    5    1     32           1

 (((— -  —) +  ——) -  3) +  —

    x    x     x            x

Step  4  :

                5

Simplify   —

                 x

Equation at the end of step  4  :

    5    1     32           1

 (((— -  —) +  ——) -  3) +  —

    x    x     x            x

Step  5  :

Adding fractions which have a common denominator :

5.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5 - (1)     4

———————  =  —

   x        x

Equation at the end of step  5  :

   4    32           1

 ((— +  ——) -  3) +  —

   x    x            x

Step  6  :

Adding fractions which have a common denominator :

6.1       Adding fractions which 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 + 32     36

——————  =  ——

  x        x

Equation at the end of step  6  :

  36          1

 (—— -  3) +  —

  x           x

Step  7  :

Rewriting the whole as an Equivalent Fraction :

7.1   Subtracting a whole from 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 :

7.2       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:

36 - (3 • x)     36 - 3x

————————————  =  ———————

     x              x  

Equation at the end of step  7  :

 (36 - 3x)    1

 ————————— +  —

     x        x

Step  8  :

Step  9  :

Pulling out like terms :

9.1     Pull out like factors :

  36 - 3x  =   -3 • (x - 12)

Adding fractions which have a common denominator :

9.2       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-3 • (x-12) + 1     37 - 3x

———————————————  =  ———————

       x               x  

Final result :

    37 - 3x

 ———————

         x  

Processing ends successfully

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step-by-step explanation: