(2/x)+(2/x-1)-(2/x-2) explain how to simplify and list restrictions.

Question

anonymous · Answer

$$\large \frac{2}{x}+\frac{2}{x-1}-\frac{2}{x-2}$$

anonymous · Answer

from here we can do the restrictions first...

anonymous · Answer

$$\large x \neq0,1,2$$

anonymous · Answer

correct?

anonymous · Answer

the common denominator for all terms is x(x-1)(x-2) right?

anonymous · Answer

ok... thanks, btw...
so to get that common denominator in that first term we must multiply (x-1)(x-2) to the numerator and denominator correct?

anonymous · Answer

yes

anonymous · Answer

so in the numerator (of that first term), you'll get 2(x-1)(x-2)

now for the second term, we must multiply x(x-2) to both numerator and denominator... correct?

anonymous · Answer

right

anonymous · Answer

what do you think we're gonna multiply to that third term?

anonymous · Answer

x

anonymous · Answer

remember, we're trying to get all these fraction a common denominator.  that last one already has a (x-2) in its denominator. so we must multiply x(x-1)

anonymous · Answer

oh k so u just have to get a common denominator right?

anonymous · Answer

yes... that's what we've been doing.. but in order to get the common denominator for each fraction, we must multiply whatever we needed in to bottom and multiply that same thing to the numerator...

anonymous · Answer

still with me?

anonymous · Answer

yea

anonymous · Answer

so then the denominator will be x(x-2)(x-1)? right?

anonymous · Answer

very good!

anonymous · Answer

and because we now have a common denominator, all we need to do is combine the numerators...

anonymous · Answer

how

anonymous · Answer

$$\large \frac {2(x-1)(x-2)+2(x)(x-2)-2(x)(x-1)}{x(x-1)(x-2)}$$

anonymous · Answer

yup... you'll have to multiply that out... it's not that bad...

anonymous · Answer

wao ok so it'll be 2(x^2-4x+2)?

anonymous · Answer

lemme check...

anonymous · Answer

yeah i have a pretty fancy calculator lol

anonymous · Answer

yeah... me too... what u got?

anonymous · Answer

calculator type...

anonymous · Answer

2(x^2-4x+2)

anonymous · Answer

yeah... that's what my calculator gave me too. i'm asking what kind of calculator u got?

anonymous · Answer

oh wolfram

anonymous · Answer

same...

anonymous · Answer

so here's your answer... wait..

anonymous · Answer

$$\large \frac {2(x^2-4x+2)}{x(x-1)(x-2)}$$
you can ask wolfram to multiply out that denominator if you want... :)

anonymous · Answer

hold up can u help me with some more complicated ones?

anonymous · Answer

post em up as a new question.. i can't scroll to much... getting dizzy..

anonymous · Answer

k