SOLUTION: I am stuck on this problem after I have tried to work it out several different ways, but am unable to get the same answer as the textbook. Your assistance would be greatly apprecia

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Question 126340This question is from textbook Mathematics for Technicians
: I am stuck on this problem after I have tried to work it out several different ways, but am unable to get the same answer as the textbook. Your assistance would be greatly appreciated. Thank you.
The problem is as follows:
2+X/X^2+X-3/3X.
This is how I have gone about this.
2+X/X^2+X-3/3X
which gives me
6X+3X^2/3X^3+X^3-3X^2/3X^3
which gives me
6X+3X^2+X^3-3X^2/3X^3
which gives me
X^3+3X^2-3X^2+6X/3X^3
which gives me
X^3+6X/3X^3
And I simply cannot see how the textbook has come up with the answer of
X^2+6/3X^2
Please would you be able to show me with an explanation as to why each step is done. Thank you so very much.
Cheers D. This question is from textbook Mathematics for Technicians

Found 2 solutions by solver91311, ilana:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bx%29%2Fx%5E2%2B%28x-3%29%2F3x

You would have had an easier time of it had you chosen the LOWEST common denominator, 3x%5E2 rather than using the simple product of the denominators 3x%5E3.

However, you have done everything else correctly, except for taking the final step.

Your answer %28x%5E3%2B6x%29%2F3x%5E3, can be rewritten by factoring as:
%28x%28x%5E2%2B6%29%29%2F%28x%283x%5E2%29%29. Then divide out the common factor:

%28cross%28x%29%28x%5E2%2B6%29%29%2F%28cross%28x%29%283x%5E2%29%29

%28x%5E2%2B6%29%2F%283x%5E2%29, which is the answer from the book. Technically, your answer was correct, it just wasn't reduced to lowest terms.


Answer by ilana(307) About Me  (Show Source):
You can put this solution on YOUR website!
You actually didn't do anything wrong, but you did do this a longer way than necessary. What I would have done is used 3x^2 as the common denominator, rather than 3x^3. So I would have multiplied the first numerator by 3 and the second by x. Then you quickly get the book's answer. However, your answer of (X^3+6X)/3X^3 simplifies to the book's answer, because you can factor out x/x (you can take an x out of each term), leaving you with (x^2+6)/3x^2. Nice job, you were so close!