Solve For X...

I tried to do this problem soo many times but cant even get close to the answer, I dont know what to do.

[(x)/(x-2)]+2=[(5x)/(x+2)]+[(3x+1)/(x^(2)-4)]

ok I know the LCD is (x+2)(x-2) and that x^(2)-4 is a perfect square that can be written as (x-2) (x+2)

But I cant get the solution it says x=3, 3/2

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 dear aisha just make sure that the denominator is equal to x²-4 everywhere... then you can forget about it (ofcourse x can't be 2 or -2) like this : [(x)(x+2)+2(x²-4)=[(5x)(x-2)+[(3x+1)] Then solve for x... can you go on from here ??? regards marlon
 Recognitions: Homework Help If you multiply through by the LCD, you'll get: (x/(x-2))(x-2)(x+2) + 2(x^2-4) = (5x/(x+2))(x-2)(x+2) + ((3x+1)/(x^2-4))(x+2)(x-2) Simplifying gives you x(x+2) + 2(x^2 - 4) = 5x(x-2) + (3x+1) Multiply it out, collect similar terms, and you'll have a quadratic. That can be factored, or you can use the Quadratic Formula. Don't forget to distribute minus signs. Does that help?

Solve For X...

 Quote by Diane_ If you multiply through by the LCD, you'll get: (x/(x-2))(x-2)(x+2) + 2(x^2-4) = (5x/(x+2))(x-2)(x+2) + ((3x+1)/(x^2-4))(x+2)(x-2) Simplifying gives you x(x+2) + 2(x^2 - 4) = 5x(x-2) + (3x+1) Multiply it out, collect similar terms, and you'll have a quadratic. That can be factored, or you can use the Quadratic Formula. Don't forget to distribute minus signs. Does that help?
YES THAT HELPS, BUT The quadratic formula I got after multiplied out and collected the like terms was -2x^(2)-x+1 and this factored out and x=-1/2 or x=-1 but the solutions were x=3, 3/2 am I wrong or is the solution wrong?
 Recognitions: Homework Help I think you're off somewhere. The quadratic I ended up with was 2x^2 - 9x + 9 = 0 which has the "proper" solutions. It's probably a simple math error. Go back through it and check it. Unsolicited advice: I have found that students often make those little errors because they're trying to go too fast. I know that the grunt work of algebra can be snore-inducing, but you need to take it slowly at first. Speed comes with experience, and experience is what you're lacking right now. You'll get there, though. All it takes is time. :)
 Thanks Diane I got it FINALLY