Solution - Reducing fractions to their lowest terms

Step  1  :

            5
 Simplify   —
            8

Equation at the end of step  1  :

                   5
  ((((3xy+5x-3y)-((—•x)•y))+7x)-8y)-7
                   8

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  8  as the denominator :

                      3xy + 5x - 3y     (3xy + 5x - 3y) • 8
     3xy + 5x - 3y =  —————————————  =  ———————————————————
                            1                    8         

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:

 (3xy+5x-3y) • 8 - (5xy)     19xy + 40x - 24y
 ———————————————————————  =  ————————————————
            8                       8        

Equation at the end of step  2  :

    (19xy + 40x - 24y)                  
  ((—————————————————— +  7x) -  8y) -  7
            8                           

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  8  as the denominator :

          7x     7x • 8
    7x =  ——  =  ——————
          1        8   

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions

 (19xy+40x-24y) + 7x • 8     19xy + 96x - 24y
 ———————————————————————  =  ————————————————
            8                       8        

Equation at the end of step  3  :

   (19xy + 96x - 24y)           
  (—————————————————— -  8y) -  7
           8                    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8  as the denominator :

          8y     8y • 8
    8y =  ——  =  ——————
          1        8   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 (19xy+96x-24y) - (8y • 8)     19xy + 96x - 88y
 —————————————————————————  =  ————————————————
             8                        8        

Equation at the end of step  4  :

  (19xy + 96x - 88y)    
  —————————————————— -  7
          8             

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  8  as the denominator :

         7     7 • 8
    7 =  —  =  —————
         1       8  

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

 (19xy+96x-88y) - (7 • 8)     19xy + 96x - 88y - 56
 ————————————————————————  =  —————————————————————
            8                           8          

Trying to factor a multi variable polynomial :

 5.3       Split       19xy + 96x - 88y - 56 
             into two 2-term polynomials
              + 96x + 19xy   and     - 88y - 56
             This partition did not result in a factorization. We'll try another one:

             19xy + 96x   and     - 88y - 56
             This partition did not result in a factorization. We'll try another one:

             19xy - 88y   and     + 96x - 56
             This partition did not result in a factorization. We'll try another one:

             19xy - 56   and     - 88y + 96x
             This partition did not result in a factorization. We'll try another one:

              - 56 + 19xy   and     - 88y + 96x
             This partition did not result in a factorization. We'll try another one:

              - 88y + 19xy   and     + 96x + 56
            All three partitions failed. Tiger finds no factorization

Final result :

  + 96x + 56