SOLUTION: I have to express the following rational expressions in lowest terms Can you please help with the following questions. I am so confused and I don't quiet understand. There are five

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Question 116864: I have to express the following rational expressions in lowest terms Can you please help with the following questions. I am so confused and I don't quiet understand. There are five questions that I tried and can't get. PLEASE HELP ME!!!!
1) x/x+xy
2)3x^2+6x/3x^2+9x
3)x^2+2x+1/x+1
4)x^2+3x-18/2x-6
5)2x^2-4x-6/x-3
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I have to express the following rational expressions in lowest terms Can you please help with the following questions. I am so confused and I don't quiet understand. There are five questions that I tried and can't get. PLEASE HELP ME!!!!
1) x%2F%28%28x%2Bxy%29%29
Factor x out in the denominator, then cancel with the x in the numerator:
x%2F%28x%281%2By%29%29 = 1%2F%28%28y%2B1%29%29
:
2)%28%283x%5E2%2B6x%29%29%2F%28%283x%5E2%2B9x%29%29
Factor out 3x in both the numerator and denominator; cancel the 3x's
%283x%28x%2B2%29%29%2F%283x%28x%2B3%29%29 = %28x%2B2%29%2F%28x%2B3%29
:
3)%28%28x%5E2%2B2x%2B1%29%29%2F%28%28x%2B1%29%29
You can factor the numerator here; cancel one of the (x+1)'s leaving:
%28%28x%2B1%29%28x%2B1%29%29%2F%28%28x%2B1%29%29 = x+1
:
4)%28%28x%5E2%2B3x-18%29%29%2F%28%282x-6%29%29
Factor the numerator and factor out 2 in the denominator, cancel the (x-3)'s:
%28%28x%2B6%29%28x-3%29%29%2F%282%28x-3%29%29 = %28%28x%2B6%29%29%2F2
:
5)%28%282x%5E2-4x-6%29%29%2F%28%28x-3%29%29
Factor the numerator:
%28%282x-6%29%28x%2B1%29%29%2F%28%28x-3%29%29
Notice now that we can factor (2x-6) in the numerator, then we can cancel
%282%28x-3%29%28x%2B1%29%29%2F%28%28x-3%29%29 = 2(x+1)
:
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Study what we did here diligently, and it will all makes sense, you can email me if you have a question about it.