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1. 
   kmieciakp Teacher
   High School - 12th Grade

   (3x-1)+[1/(3x-1)]=5

   (3x-1)(3x-1) + 1 = 5(3x-1)

   9x^2 -6x + 1 +1=15x-5

   9x^2 -21x +2 = - 5

   9x^2 -21x +7 = 0

   (       )(       )=0

   check the equation--it doesn't factor--see if you wrote it down right please-- I think you meant = negative 5--then it would work fine

   then send it back to me . . .I love doing these things

   thanks

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   Posted by kmieciakp on Tuesday March 3, 2009 at 11:17 AM
   
   

2. 
   neela Teacher
   Graduate School

   eNotes Editor

   (3x-1)+{1/(3x-1)}=5

   Mutiply by the denominator (3x-1) to get rid of the fractional form.

   (3x-1)^2+1=5(3x-1)

   9x^2-6x +2=15x-5.

   9x^2-6x-15x+7=0

   9x^2-21x+7 is a quadratic equation of the form ax^2+bx+c=0 whose roots are given by

   x=[b-sqrt(b^2-4ac)}/(2a).

   a=9,b=-21 and c=7. Substing in the quadratic equation we get the roots:

   x= [-(-21) +or- sqrt(21^2-4*9*7)}/(2*9}

   x=[7+sqrt21]6   or  x=[7-sqrt21]/6

   x=1.9304approximately,  or  x=0.4029 approx.

   You can put back int he original equations

    

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   Posted by neela on Thursday June 11, 2009 at 5:55 AM