1. ## Equation Help

I'm having a bit of trouble with this problem.

Solve the equation.
3/2x-1/x+1=1/x(3x+3)

Here is an image of the problem if the equation above is not clear
http://i1198.photobucket.com/albums/...g?t=1297473401

2. Is this for an online quiz?

3. No, just practice.

4. Ok, that's fine. What ideas have you had so far?

5. Clearing out the denominators by multiplying the whole equation by (2x) (x+1) x(3x+3)

6. Go for it; that idea sounds good. Post what you get, and we can help you from there.

7. After multiplying by (2x) (x+1) x(3x+3) and simplifying I get 3x^3+12x^2+9x=2x^2+2x. This is the part where I'm sort of lost; I'm not sure if I made a mistake or not.

8. No mistakes so far. Notice that every single term has an x in it. Since x = 0 is not a solution of the original equation (you'd divide by zero in the first term!), you can cancel a power of x from every term. What do you suppose you could do next?

9. By canceling a power of x from every term do you mean just taking an x out of every term? So 3x^3-10x^2+7x=0 would be 3x^2-10x+7=0?

10. Exactly. Then what?

11. Could I use the quadratic equation at this point?

12. Sure, why not? What's the result?

13. Using the quadratic equation and substituting 3=a, -10=b and 7=c I get x=7/3 and x=6/6 (1)

14. I think your answers are off by a minus sign. If you're ever in doubt, plug your solutions back into the equation and see if they satisfy it.

15. Using 3x^2-10x+7 in the quadratic formula I get x= 10(plus or minus) 4/6 Is that right or did I make a mistake before that?

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