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Mathematics
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May 25th, 2015

(5x^7/7-x) / (7x-1/49-x^2)

Raise  x to the  2nd power
       (x7)   x      1
  (((5•————)-(—•x))-——)-x2
        7     7     49
           x      
 Multiply  —  by  x
           7      

  x1 multiplied by x1 = x(1 + 1) = x2

       (x7)  x2   1
  (((5•————)-——)-——)-x2
        7    7   49
 Raise  x to the  7th power
         x7     x2      1     
  (((5 • ——) -  ——) -  ——) -  x2
         7      7      49     
           5x7     x2
Simplify   ———  -  ——
            7      7 

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

 5x7 - (x2)     5x7 - x2
 ——————————  =  ————————
     7             7    
   (5x7 - x2)     1     
  (—————————— -  ——) -  x2
       7         49     
           5x7-x2      1
Simplify   ——————  -  ——
             7        49

 Pull out like factors :


  5x7 - x2 =  x2 • (5x5 - 1) 

  Find the Least Common Multiple 

  Least Common Multiple: 
  49 

  Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      x2 • (5x5-1) • 7
   ——————————————————  =   ————————————————
         L.C.M                    49       

   R. Mult. • R. Num.       1
   ——————————————————  =   ——
         L.C.M             49

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:

 x2 • (5x5-1) • 7 - (1)     35x7 - 7x2 - 1
 ——————————————————————  =  ——————————————
           49                     49      
  (35x7 - 7x2 - 1)    
  ———————————————— -  x2
         49           
           35x7-7x2-1     
Simplify   ——————————  -  x2
               49         

Rewrite the whole as a fraction using  49  as the denominator :

           x2     x2 • 49
     x2 =  ——  =  ———————
           1        49   
 (35x7-7x2-1) - (x2 • 49)      35x7 - 56x2 - 1
 ————————————————————————  =  ———————————————
            49                      49       

Answer 

  35x7 - 56x2 - 1
  ———————————————
        49      

May 26th, 2015

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May 25th, 2015
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