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Math Help - Exponents on polynomials

  1. #1
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    Question Exponents on polynomials

    I'm having trouble with this problem.

    The only way I can get the answer the book gives is to illegally remove the exponent of 1/2 from the 1st term.

    Problem: (2x+1)^(1/2) + (x+3)(2x+1)^(-1/2)

    my attempt:
    =(2x+1)^(1/2) + ((x+3) / ((2x + 1)^(1/2))
    (I don't see any like terms here unless I remove the exponent)

    Book's answer: (3x+4) / (sqrt(2x+1))

    Another question: I see that I should move
    (2x+1)^(-1/2) to the denominator because of the negative exponent. When I do this, does it go in the denominator of all the other terms, or just in the den of (x+3)?

    Please explain what I'm doing wrong. Thanks alot!!

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  2. #2
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     (2x+1)^{\frac{1}{2}} + (x+3)(2x+1)^{\frac{-1}{2}}=(2x+1)^{\frac{1}{2}} + \frac{(x+3)}{(2x+1)^{\frac{1}{2}}}=\frac{(2x+1) +(x+3)}{(2x+1)^{\frac{1}{2}}}<br />

    now simplify the numerator
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  3. #3
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    Quote Originally Posted by dwatkins741 View Post
    I'm having trouble with this problem.

    The only way I can get the answer the book gives is to illegally remove the exponent of 1/2 from the 1st term.

    Problem: (2x+1)^(1/2) + (x+3)(2x+1)^(-1/2)

    my attempt:
    =(2x+1)^(1/2) + ((x+3) / ((2x + 1)^(1/2))
    (I don't see any like terms here unless I remove the exponent)

    Book's answer: (3x+4) / (sqrt(2x+1))

    Another question: I see that I should move (2x+1)^(-1/2) to the denominator because of the negative exponent. When I do this, does it go in the denominator of all the other terms, or just in the den of (x+3)?

    Please explain what I'm doing wrong. Thanks alot!!

    \sqrt{2x+1}+\frac{x+3}{\sqrt{2x+1}}=\frac{2x+1+x+3  }{\sqrt{2x+1}}=\frac{3x+4}{\sqrt{2x+1}} , via \sqrt{a}+\frac{1}{\sqrt{a}}=\frac{a+1}{\sqrt{a}} ... common denominator and stuff.

    Tonio
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  4. #4
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    Thumbs up That's new to me

    That formula you gave, Tonio, was totally new to me. I never knew you could do that with radicals. I tested it out and it works. Thanks alot. Very helpful.
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  5. #5
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    Quote Originally Posted by dwatkins741 View Post
    I'm having trouble with this problem.

    The only way I can get the answer the book gives is to illegally remove the exponent of 1/2 from the 1st term.

    Problem: (2x+1)^(1/2) + (x+3)(2x+1)^(-1/2)

    my attempt:
    =(2x+1)^(1/2) + ((x+3) / ((2x + 1)^(1/2))
    (I don't see any like terms here unless I remove the exponent)

    Book's answer: (3x+4) / (sqrt(2x+1))

    Another question: I see that I should move
    (2x+1)^(-1/2) to the denominator because of the negative exponent. When I do this, does it go in the denominator of all the other terms, or just in the den of (x+3)?

    Please explain what I'm doing wrong. Thanks alot!!

    I expect you've been asked to simplify this... To simplify expressions involving fractions, you need a common denominator.

    \sqrt{2x + 1} + \frac{x + 3}{\sqrt{2x + 1}} = \frac{\sqrt{2x + 1}\sqrt{2x + 1}}{\sqrt{2x + 1}} + \frac{x + 3}{\sqrt{2x + 1}}

     = \frac{2x + 1}{\sqrt{2x + 1}} + \frac{x + 3}{\sqrt{2x + 1}}

     = \frac{2x + 1 + x + 3}{\sqrt{2x + 1}}

     = \frac{3x + 4}{\sqrt{2x + 1}}.


    I choose to write fractions with rational denominators though, so to clean it up even more...

     = \frac{(3x + 4)\sqrt{2x + 1}}{2x + 1}.
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