SOLUTION: We are going over Rational expressions. My problem is I don't know what to do after I get the answer for the denominator. But unfortunately for this one I can't even get that far!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: We are going over Rational expressions. My problem is I don't know what to do after I get the answer for the denominator. But unfortunately for this one I can't even get that far!       Log On


   

Question 869708: We are going over Rational expressions. My problem is I don't know what to do after I get the answer for the denominator. But unfortunately for this one I can't even get that far! Can you help me with steps to get through this problem?
5/x^2+5x+6 + 2/x+3
So far I have 5/(x+3)(x+2) + 2(x+2)/x+3(x+2)
Found 4 solutions by Alan3354, mananth, jim_thompson5910, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5/x^2+5x+6 + 2/x+3
So far I have 5/(x+3)(x+2) + 2(x+2)/x+3(x+2)
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Since the DEN's are the same, you can add the NUMs.
5/(x+3)(x+2) + 2(x+2)/x+3(x+2)
= 5/(x+3)(x+2) + (2x+4)/(x+3)(x+2)
= (2x+9)/(x+3)(x+2)

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
5/x^2+5x+6 + 2/x+3

5/((x+3)(x+2)) +2/(x+3)

(5+2(x+2))/((x+3)(x+2))
(2x+7)/(x+3)(x+2))

(2x+7)/(x+3)(x+2))

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
So far, so good. Let's finish up.


5%2F%28%28x%2B3%29%28x%2B2%29%29%2B%282%28x%2B2%29%29%2F%28%28x%2B3%29%28x%2B2%29%29


%285%2B2%28x%2B2%29%29%2F%28%28x%2B3%29%28x%2B2%29%29 We are able to add the fractions only if the denominators are the same (they are, so we can go ahead)


%285%2B2x%2B4%29%2F%28%28x%2B3%29%28x%2B2%29%29


%282x%2B9%29%2F%28%28x%2B3%29%28x%2B2%29%29

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Not well written. Grouping symbols MUST BE used in the proper positions:

Your step appears to indicate three separate summands:
5/(x^2+5x+6) + 2/x+3

and as rendered appear this way:
5%2F%28x%5E2%2B5x%2B6%29%2B+2%2Fx%2B3+

Maybe that is not what you really have. Maybe you really have this:
5%2F%28x%5E2%2B5x%2B6%29%2B2%2F%28x%2B3%29. I will work through part of this one.
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5%2F%28%28x%2B2%29%28x%2B3%29%29%2B2%2F%28x%2B3%29, you see LCD is (x+2)(x+3). Need to multiply the second summand by 1.
5%2F%28%28x%2B2%29%28x%2B3%29%29%2B%282%2F%28x%2B3%29%29%28%28x%2B2%29%2F%28x%2B2%29%29
%285%2B2%28x%2B2%29%29%2F%28%28x%2B2%29%28x%2B3%29%29
%285%2B2x%2B4%29%2F%28%28x%2B2%29%28x%2B3%29%29
%282x%2B9%29%2F%28%28x%2B2%29%28x%2B3%29%29
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and you can finish that by simplifying the denominator, which you already know from the start, the LCD.