How to factor (x/x-2)-(x+2/x)

Question

my answer is -x^2-x-2/x

and (3+sq rt 5)*(3-sq rt 5)
my answers are either 4 or 3*sq rt 5^2

are any of these right?

Thanks so much for all of your help.

Answer 1

I have a feeling your question is

x/(x-2) - (x+2)/x

Factoring doesn't make much sense, more than likely it says "simplify", am I right?

for (3 + √5)(3 - √5)

You should recognize the 'difference of squares' patter, or you could just expand it

= 9 - 5 = 4

4 is the only answer

Answer 2

Yes, you are right. It does say simplify.

Answer 3

back to x/(x-2) - (x+2)/x then

common denominator is x(x-2)

so x/(x-2) - (x+2)/x
= [x^2 - (x+2)(x-2)] / [x(x-2)]
= (x^2 - x^2 + 4)/[x(x-2)]
= 4/(x(x-2))

Answer 4

I changed my answer to
x/(x-2) - (x+2)/x to 4/x(x-2)

Is that right?

Answer 5

got it, thanks!