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Math Help - solving rational equations

  1. #1
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    Exclamation solving rational equations

    x-1 + x-3 = x+13
    x+5 x+2


    If someone could do this step by step would help me a ton and would be appreciated.

    I am confused about the LCD is it LCD=(x+5),(x+2)?
    because when I do on the right side of the = it is (x+13)(x+5)(x+2) and I think thats wrong because she said in our class we wont foil three sets of brackets.
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  2. #2
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    Quote Originally Posted by brentwoodbc View Post
    x-1 + x-3 = x+13
    x+5 x+2


    If someone could do this step by step would help me a ton and would be appreciated.

    I am confused about the LCD is it LCD=(x+5),(x+2)?
    because when I do on the right side of the = it is (x+13)(x+5)(x+2) and I think thats wrong because she said in our class we wont foil three sets of brackets.
    FOIL the last 2 sets first, you get

    (x+13)(x^2 + 7x + 10)

    Then multiply everything in the first bracket by everything in the second, so it becomes

    x(x^2 + 7x + 10) + 13(x^2 + 7x + 10).
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  3. #3
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    Quote Originally Posted by Prove It View Post
    FOIL the last 2 sets first, you get

    (x+13)(x^2 + 7x + 10)

    Then multiply everything in the first bracket by everything in the second, so it becomes

    x(x^2 + 7x + 10) + 13(x^2 + 7x + 10).
    thank you very much I just need to think about this for a minute the answer is
    -7, 11 +/-sqrt37
    2

    just need to figure that out thanks agian though.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    FOIL the last 2 sets first, you get

    (x+13)(x^2 + 7x + 10)

    Then multiply everything in the first bracket by everything in the second, so it becomes

    x(x^2 + 7x + 10) + 13(x^2 + 7x + 10).
    thank you very much I just need to think about this for a minute the answer is
    -7, 11 +/-sqrt37
    --------2

    just need to figure that out thanks agian though. because u get an x^3 term and you need to factor it .
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  5. #5
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    Quote Originally Posted by brentwoodbc View Post
    thank you very much I just need to think about this for a minute the answer is
    -7, 11 +/-sqrt37
    --------2

    just need to figure that out thanks agian though. because u get an x^3 term and you need to factor it .
    Once you've expanded everything and equated it to 0, you should get a linear factor and a quadratic factor.

    Then you solve the linear factor using the null factor law and the quadratic factor using the null factor law and quadratic formula.
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  6. #6
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    here's your solution...

    the LCD is (x+5)(x+2)

    if you mulitply ech term by the LCD you will eliminate the fractions and have (x-1)(x+2)+(x-3)(x+5)=(x+13)(x+5)(x+2)

    FOIL the 1st and 2nd terms and mulitply the last terms and you now have:
    x^2+2x-x-2+x^2+5x-3x-15+x^3+7x^2+10x+13x^2+91x+130

    Combine like terms on each side and you have:
    2x^2+3x-17=x^3+20x^2+101x+130

    Get all terms to the left side and you now have:
    -x^3-18x^2-98x-147=0

    from here use synthetic division or factor by grouping...hope this helped!
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