Question

Show all work to simplify 2/x - 2/x-1 + 2/x-2 . Use complete sentences to explain how to simplify this expression. Remember to list all restrictions.

Answer 1

Crap. restrictions are going to give you some trouble

Answer 2

i hate restrictions but i know how to find them from the solution :P

Answer 3

get a common denominator (x)(x+1)(x+2)


[2(x+1)(x+2) +2(x)(x+2) -2(x)(x+1)]/(x)(x+1)(x+2)

expand and simplify

[2x^2 +6x + 4 + 2x^2 +4x -2x^2 -2x]/(x)(x+1)(x+2)

collect like terms

[2x^2 +8x +4]/(x)(x+1)(x+2)

leaves

2[x^2 +4x +2]/(x)(x+1)(x+2)

does that look right ?

Answer 4

:O You just made me seem stupid D:< Jk

Answer 5

looks good. now the restrictions.

Answer 6

2/x-2/x-1+2/x-2
=2/x-2*x-1+2/x-2
=2x-2/x-1+2/x-2

Answer 7

the restrictions should be ... -1 & -2 , right ?

Answer 8

you forgot the x that is in denominator

Answer 9

oh right ... umm ... shoot now im not sure ..

Answer 10

it's fine you did x+1=0 and x+2=0 to get -1 and -2
right?

Answer 11

yes

Answer 12

ok
but your denominator is
\[ \large x(x+1)(x+2) \]
if you put
\[ \large x(x+1)(x+2)=0 \]
you get x=0 or x+1=0 or x+2=0.
so u missed the x

Answer 13

okay thanks :)

Answer 14

just wait!

Answer 15

restrictions are just instructions to keep you from dividing by 0
so if you have 3/x the restriction is x≠0

Answer 16

your original problem is
\[ \large \frac{2}{x}-\frac{2}{x-1}+\frac{2}{x-2} \]
correct this in what u didi before

Answer 17

if you have 3/(x-1) you can not have x=1 because x-1 would become 1-1=0 and that is bad