Solving for X

Date: 01/13/97 at 03:51:08
From: Yaroslav Greshilov
Subject: Equation

I need help with this very much. Sorry, my English is not very good 
because I'm Russian, but I hope you will help me.

   3(x*x)-2x+2 = 2/(3(x*x)-2x+1)

Find answers to this equation.

Date: 01/13/97 at 13:26:51
From: Doctor Rob
Subject: Re: Equation

Thanks for your question.  Your English is good enough, and certainly
a lot better than my Russian!
   
I can think of two ways to solve this equation:

 A)  Let y = 3*x^2 - 2*x, so that the equation reads:

                 y + 2 = 2/(y + 1)

     Now multiply both sides by (y + 1): 

       (y + 2)*(y + 1) = 2

     Subtract 2 from both sides, and expand:

     y^2 + 3*y + 2 - 2 = 0
             y^2 + 3*y = 0
             y*(y + 3) = 0
            y = 0 or y = -3

     Now put these equations in y in terms of x:

     3*x^2 - 2*x = 0  or  3*x^2 - 2*x = -3
     x*(3*x - 2) = 0  or  3*x^2 - 2*x + 3 = 0

               x = 0  or  
               x = 2/3  or  
               x = (1 + 2*Sqrt[-2])/3  or
               x = (1 - 2*Sqrt[-2])/3

 B) Multiply both sides by the denominator on the right, bring all
    terms to the left side, expand and gather like terms.  You will
    have a fourth degree equation.  Factor the left side and set each
    factor equal to zero and solve for x in each part.

If you need more help, write back again.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/