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

Question

anonymous · Answer

attachment

anonymous · Answer

PLEASE HELP :)

anonymous · Answer

Your expression looks like this: $${2 \over x} + {2 \over x+1} - {2 \over x+2}$$
Do you see any common factor, off the top?

anonymous · Answer

yea 2

anonymous · Answer

Common denominator. Then, you can add/subtract.

anonymous · Answer

ok, you can factor it out then so it looks like $$ 2*({1 \over x} + {2 \over x+1} - {1 \over x+2})$$ And yeah, then follow petewe's advice and find the common denom.

campbell_st · Answer

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)

anonymous · Answer

k thaks

anonymous · Answer

Yet another way to simplify is to see that 2/x appears on every term. In order for the equation be the same after factoring out 2/x, there must be a, b, c such that:
$$(2/x)*(a + b - c) = (2/x) + (2/(x+1)) - (2/(x+2))$$You can solve it on a one-to-one relation with these equations:
(2/x)*a = (2/x) => a = 1
(2/x)*b = (2/(x+1)) => b = (x/(x+1))
(2/x)*c = (2/(x+2)) => c  = (x/(x+2)), and the equation then becomes:$$(2/x)*(1 + x/(x+1) - x/(x+2))$$