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### Solving for X

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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)

```

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

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/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra

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