# Math Help - difficulty with quadratic fraction problem

1. ## 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

2. 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?

3. 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

4. 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.

5. ok i shall crack on with that. many thanks!

6. 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.

7. just to re-iterate, the original equation was:

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

8. 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

9. Thankyou very much. after some reworking to get how it should look, i can see where i was going wrong now!