# difficulty with quadratic fraction problem

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• Feb 16th 2011, 10:55 AM
euphmorning
difficulty with quadratic fraction problem
Hello all. i'm currently trying to solve this equation:

x-1 / x - 4 / x+3 = 0

my skills with rational equations are very limited, and find myself getting getting frustratingly confused alot !

i've got as far as :

(x-1)(x+3) / x(x+3) - 4x / x(x+3)

i'm hoping someone can give me some insight into solving this as i'm lost as to what i need to do next.

Cheers
• Feb 16th 2011, 10:59 AM
e^(i*pi)
If it's $\dfrac{x-1}{x} + \dfrac{4}{3} = 0$

Multiply through by the lowest common denominator and simplify the linear equation you're left with

Do you know what the LCD is?
• Feb 16th 2011, 11:11 AM
euphmorning
Hi there, well in terms of my equation, i've got the LCD as x(x+3) . see my original post, is this so far so good?

kind thanks
• Feb 16th 2011, 11:17 AM
HallsofIvy
So your equation is $\frac{x- 1}{x}- \frac{4}{x+ 3}= 0$?

Yes, the LCD is x(x+3). Multiply each part of the equation by that and you will get rid of the fractions.
• Feb 16th 2011, 11:21 AM
euphmorning
ok i shall crack on with that. many thanks!
• Feb 17th 2011, 10:12 AM
euphmorning
hello once again.. ok, i feel i've moved on a little bit with this but seemingly got stuck again as i cant seem to get a quadratic form..

so i've muliplied by x(x+3) to give:

x-1(x(x+3)) / x - 4(x(x+3)) / (x+3)

cancelling i then get:

x-1(x+3) - 4x

expanding :

x - x - 3 - 4x ...

i'm lost! help appreciated. thanks in advance.
• Feb 17th 2011, 10:15 AM
euphmorning
just to re-iterate, the original equation was:

x-1 / x - 4 / x+3 = 0
• Feb 17th 2011, 12:18 PM
BobBali
After you canceld out the denominators with LCD x(x+3) we get>

[tex](x+3)(x+1) - 4x = 0 [\math]

[tex] x^2 - x + 3x - 3 - 4x = 0 [\math]

[tex] x^2 -2x -3 = 0 [\math]

Now factorize > [tex] (x -3) (x +1) = 0 [\math]

Therefore, x=3 and x=-1
• Feb 17th 2011, 03:26 PM
euphmorning
Thankyou very much. after some reworking to get how it should look, i can see where i was going wrong now!