## anonymous one year ago Solve for x: 5 over quantity x squared minus 4 plus 2 over x equals 2 over quantity x minus 2. x = 8 x = –4 x = 8 and x = –4 No Solution

1. anonymous

$x: \frac{ 5}{ x^2 - 4 } + \frac{ 2 }{ x } = \frac{ 2 }{ x - 2 }$

2. anonymous

@paki @freckles

3. anonymous

@Compassionate

4. anonymous

@sweetburger

5. sweetburger

get each of the denominators the same so you can add and subtract them together

6. Ciarán95

I'm not sure about this one...the first thing I did was to notice that we can factorise x^-4 into (x+2)(x-2) - the difference of two squares. So, the equation becomes: $\frac{ 5 }{ (x+2)(x-2) } + \frac{ 2 }{ x } = \frac{ 2 }{ x-2 }$ Now, multiplying across by (x-2) leaves us with: $\frac{ 5 }{ x-2 } +\frac{ 2(x-2) }{ x } = 2$ We can then form the left-hand side as one fraction by using the lowest common denominator of the two fractions, (x-2)(x): $\frac{ 5x + 2(x-2)(x+2) }{x(x-2) } = 2$ After quite a tricky rearrangement process to leave us with x on its own (all the x^2 terms will cancel out), you should be able to obtain one of the possible answers given in the question. Hope that helps! :)

7. sweetburger

Looks good @Ciarán95