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Math Help - Adding and subtracting rational expressions. Please help?

  1. #1
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    Adding and subtracting rational expressions. Please help?

    I have a math problem and the answer to it. The only problem I have is that I cannot figure out how to get the answer given. I have posted a picture of the math problem below please help me understand this math problem. I would greatly appreciate it.
    Attached Thumbnails Attached Thumbnails Adding and subtracting rational expressions. Please help?-2012-11-14_18-14-52_169.jpg  
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  2. #2
    Senior Member MacstersUndead's Avatar
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    Re: Adding and subtracting rational expressions. Please help?

    Note that 5p^2 + 16p - 16 = (p+4)(5p-4), which helps somewhat. Make it a habit to try and factorize quadratics when given this kind of problem to aid in finding easy common denominators.

    In this problem, we could make the common denominator of each term (4-5p)(5p-4)(p+4).

    For example, this would mean that in the first term the numerator would be 8(5p-4)(p+4).
    Do the same for the other two terms.
    Combine the terms.
    Simplify the numerator.
    Divide by monomials ex. (4-5p),(5p-4),(p+4) if possible.

    done.
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  3. #3
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    Re: Adding and subtracting rational expressions. Please help?

    Im still confused could you elaborate a little more?
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  4. #4
    Senior Member MacstersUndead's Avatar
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    Re: Adding and subtracting rational expressions. Please help?

    What would you like elaborated?
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    Re: Adding and subtracting rational expressions. Please help?

    Adding and subtracting rational expressions. Please help?-math-help.jpg here is where im stuck I got to this point I dont know what to do now?
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  6. #6
    Senior Member MacstersUndead's Avatar
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    Re: Adding and subtracting rational expressions. Please help?

    Assuming that your expansions are correct, all that's left to do on the numerator is to collect like terms. In this example, we can reorder the numerator as

    40p^2 - 10p^2 -5p^2 + 160p - 32p -8p -40p + 4p + 20p - 128 + 32 - 16 which can be rewritten as
    (40 - 10 - 5)p^2 + (160 - 32 - 8 - 40 + 4 + 20)p + (-128 + 32 - 16)

    Simplify, and then you're done.
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    Re: Adding and subtracting rational expressions. Please help?

    alright so i have combined everything and I am stuck again. 25p^2+104p-112/(4-5p)(5p-4)(p+4) I dont know what to do from here to get the answer am I even close it says the answer is -9p-44/(5p-4)(p+4)
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  8. #8
    Senior Member MacstersUndead's Avatar
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    Re: Adding and subtracting rational expressions. Please help?

    (-9p-44) * (4-5p) = 45p^2 - 36p +140p - 176 = 45p^2 -104p - 176 , so somewhere along the way you did not expand correctly. You are close, however. Try again from scratch and use the same general process I introduced. If you cannot solve it after a meaningful effort, I'll write a full detailed solution.
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    Re: Adding and subtracting rational expressions. Please help?

    alright so i have combined everything and I am stuck again. 25p^2+104p-112/(4-5p)(5p-4)(p+4) I dont know what to do from here to get the answer am I even close it says the answer is -9p-44/(5p-4)(p+4)
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    Re: Adding and subtracting rational expressions. Please help?

    Idk what to do. Ive been working on this same problem all day for like probably 5 hours now. Could u help me out and give me a detailed solution
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  11. #11
    Senior Member MacstersUndead's Avatar
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    Re: Adding and subtracting rational expressions. Please help?

    Alright, here's a detailed answer. You must have done something wrong in the middle steps, but the concept of common denominator is still the same. Let us consider each term seperately and simplify

    \frac{8}{4-5p} = \frac{8(5p-4)(p+4)}{(4-5p)(5p-4)(p+4)} = \frac{40p^2 -32p + 160p - 128}{(4-5p)(5p-4)(p+4)}
    \frac{-2}{5p-4} = \frac{-2(4-5p)(p+4)}{(4-5p)(5p-4)(p+4)} = \frac{10p^2 + 32p - 32}{(4-5p)(5p-4)(p+4)}
    \frac{(p-4)}{(5p-4)(p+4)} = \frac{(p-4)(4-5p)}{(4-5p)(5p-4)(p+4)} = \frac{24p - 5p^2 - 16}{(4-5p)(5p-4)(p+4)}

    Combining the fractions and like terms like we did before we get
    \frac{45p^2 + 184p - 176}{(4-5p)(5p-4)(p+4)}

    While not immediately obvious
    \frac{45p^2 + 184p - 176}{(4-5p)(5p-4)(p+4)} = \frac{-9p-44}{(5p-4)(p+4)}

    since (4-5p) divides (45p^2 + 184p - 176). You can use polynomial long division to verify.

    If you have any more questions, let me know. I still want you to practice your skills and challenge your knowledge base so you are ready for exams EDIT:// computation error.
    Last edited by MacstersUndead; November 14th 2012 at 06:19 PM.
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  12. #12
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    Re: Adding and subtracting rational expressions. Please help?

    Code:
         p - 4            8          2
    =============== - ======== - ========
    (p + 4)(5p - 4)    5p - 4     5p - 4
    
    
     p - 4      8     2
    ======== - === - ===
    k(p + 4)    k     k
    Since 8/(4 - 5p) = -8/(5p - 4), rearrange terms as I show above;
    then, to keep "as simple as possible", let k = 5p - 4 (as above).

    Now do the "work", then replace k by 5p - 4 : get my drift?
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