Solution - Reducing fractions to their lowest terms

Step  1  :

            294
 Simplify   ———
             x 

Equation at the end of step  1  :

                           294     
  (x - 7) • (((3x - 50) -  ———) -  7)
                            x      

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

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

                3x - 50     (3x - 50) • x
     3x - 50 =  ———————  =  —————————————
                   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:

 (3x-50) • x - (294)     3x2 - 50x - 294
 ———————————————————  =  ———————————————
          x                     x       

Equation at the end of step  2  :

             (3x2 - 50x - 294)    
  (x - 7) • (————————————————— -  7)
                     x            

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

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

Trying to factor by splitting the middle term

 3.2     Factoring  3x² - 50x - 294 

The first term is,  3x²  its coefficient is  3 .
The middle term is,  -50x  its coefficient is  -50 .
The last term, "the constant", is  -294 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -294 = -882 

Step-2 : Find two factors of  -882  whose sum equals the coefficient of the middle term, which is   -50 .

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

 3.3       Adding up the two equivalent fractions

 (3x2-50x-294) - (7 • x)     3x2 - 57x - 294
 ———————————————————————  =  ———————————————
            x                       x       

Equation at the end of step  3  :

            (3x2 - 57x - 294)
  (x - 7) • —————————————————
                    x        

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3x² - 57x - 294  =   3 • (x² - 19x - 98) 

Trying to factor by splitting the middle term

 5.2     Factoring  x² - 19x - 98 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -19x  its coefficient is  -19 .
The last term, "the constant", is  -98 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -98 = -98 

Step-2 : Find two factors of  -98  whose sum equals the coefficient of the middle term, which is   -19 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  3 • (x - 7) • (x2 - 19x - 98)
  —————————————————————————————
                x