SOLUTION: umm, hello??? can anybody help me with my algebra problem?? the direction is to "Simplify each of the following complex rational expressions. 2 - 1/[

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Question 117079: umm, hello??? can anybody help me with my algebra problem??
the direction is to "Simplify each of the following complex rational expressions.
2 - 1/[2+[1 /{(x-1)/x}]

I'm very sorry because i don't know how to type it in. But i hope you could give me your generous help by answering the question.. thnx!!
_good luck_
_angELz_
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29 Start with the given expression


2-1%2F%282%2Bx%2F%28x-1%29%29%29 Simplify 1%2F%28%28x-1%29%2Fx%29 to get x%2F%28x-1%29. What's really happening is I'm taking the reciprocal of this fraction



2-1%2F%28%282%29%28%28x-1%29%2F%28x-1%29%29%2Bx%2F%28x-1%29%29%29 Multiply 2 by %28x-1%29%2F%28x-1%29


2-1%2F%28%282x-2%29%2F%28x-1%29%2Bx%2F%28x-1%29%29%29 Distribute

2-1%2F%28%282x-2%2Bx%29%2F%28x-1%29%29%29 Combine the fractions


2-1%2F%28%283x-2%29%2F%28x-1%29%29%29 Combine like terms


2-%28x-1%29%2F%283x-2%29 Simplify 1%2F%28%283x-2%29%2F%28x-1%29%29 to get %28x-1%29%2F%283x-2%29 by once again taking the reciprocal




2%28%283x-2%29%2F%283x-2%29%29-%28x-1%29%2F%283x-2%29 Multiply 2 by %283x-2%29%2F%283x-2%29


%286x-4%29%2F%283x-2%29-%28x-1%29%2F%283x-2%29 Distribute


%286x-4-%28x-1%29%29%2F%283x-2%29 Combine the fractions



%286x-4-x%2B1%29%2F%283x-2%29 Distribute the negative


%285x-3%29%2F%283x-2%29 Combine like terms



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Answer:

So 2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29 simplifies to %285x-3%29%2F%283x-2%29. In other words, 2-1%2F%282%2B1%2F%28%28x-1%29%2Fx%29%29=%285x-3%29%2F%283x-2%29. You can verify this if you graph the original and the simplified expressions and you'll notice that they overlap. So this visually verifies our answer.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
2 - 1/[2+[1 /{(x-1)/x}]
1*x/(x-1)=x/(x-1)
1%2F%282%2B%28x%2F%28x-1%29%29%29=1%2F%282x-2%29%2Bx%2F%28x-1%29=1%2A%28x-1%29%2F%283x-2%29
2-(x-1)/(3x-2)
=2(3x-2)-(x-1)/(3x-2)
=6x-4-x+1/(3x-2)
=5x-3/3x-2
.
I think, maybe.
.
Ed