Question

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

Answer 1

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

Answer 2

@paki @freckles

Answer 3

@Compassionate

Answer 4

@sweetburger

Answer 5

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

Answer 6

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! :)

Answer 7

Looks good @Ciarán95