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Math Help - Simplfying Algebra!!

  1. #1
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    Simplfying Algebra!!

    Simplify (x+2)[\frac{\frac{-3}{2}}{(3x+1)^(1.5)}]+\frac{1}{\sqrt{3x+1}}

    >>>>;;;;Note that 1.5 is a power of 3x+1;;;;<<<<
    Last edited by Punch; February 11th 2010 at 09:42 PM.
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  2. #2
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    Hello Punch
    Quote Originally Posted by Punch View Post
    Simplify (x+2)[\frac{\frac{-3}{2}}{(3x+1)^(1.5)}]+\frac{1}{\sqrt{3x+1}}

    >>>>;;;;Note that 1.5 is a power of 3x+1;;;;<<<<
    If I re-write the question, I think it is: Simplify:
    (x+2)\left(\frac{-\frac{3}{2}}{(3x+1)^{1.5}}\right)+\frac{1}{\sqrt{3  x+1}}
    First, note that the (x+2) is multiplying the first fraction, so it goes on top; the -\tfrac32 can be written with the -3 on top and the 2 underneath. So we get:
    =\frac{-3(x+2)}{2(3x+1)^{1.5}}+\frac{1}{\sqrt{3x+1}}
    Do you see how that works?

    Then (...)^{1.5} = (...)^1\times(...)^{0.5}=(...)\sqrt{(...)}.

    So the next stage is:
    =\frac{-3(x+2)}{2(3x+1)\sqrt{3x+1}}+\frac{1}{\sqrt{3x+1}}
    OK. Now find the lowest common denominator, which is 2(3x+1)\sqrt{3x+1}. So, writing the second fraction with this denominator, we get:
    =\frac{-3(x+2)}{2(3x+1)\sqrt{3x+1}}+\frac{2(3x+1)}{2(3x+1)  \sqrt{3x+1}}
    Now combine the fractions over a single denominator and simplify:
    =\frac{-3(x+2)+2(3x+1)}{2(3x+1)\sqrt{3x+1}}

    =\frac{3x-4}{2(3x+1)\sqrt{3x+1}}
    which you can write as:
    =\frac{3x-4}{2(3x+1)^{1.5}}
    if you like.

    Grandad
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  3. #3
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    Quote Originally Posted by Punch View Post
    Simplify (x+2)[\frac{\frac{-3}{2}}{(3x+1)^(1.5)}]+\frac{1}{\sqrt{3x+1}}

    >>>>;;;;Note that 1.5 is a power of 3x+1;;;;<<<<
    (x+2)\left[\frac{\frac{-3}{2}}{(3x+1)^{1.5}}\right]+\frac{1}{\sqrt{3x+1}}

    Split the exponent of 1.5 into 1 + 0.5:

    \left[\frac{-\frac{3}{2} \cdot (x+2)}{(3x+1) \cdot \sqrt{3x+1}}\right]+\frac{1}{\sqrt{3x+1}}

    Determine the common denominator of the fractions and combine the numerators.
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  4. #4
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    Quote Originally Posted by Grandad View Post
    Hello PunchIf I re-write the question, I think it is: Simplify:
    (x+2)\left(\frac{-\frac{3}{2}}{(3x+1)^{1.5}}\right)+\frac{1}{\sqrt{3  x+1}}
    First, note that the (x+2) is multiplying the first fraction, so it goes on top; the -\tfrac32 can be written with the -3 on top and the 2 underneath. So we get:
    =\frac{-3(x+2)}{2(3x+1)^{1.5}}+\frac{1}{\sqrt{3x+1}}
    Do you see how that works?

    Then (...)^{1.5} = (...)^1\times(...)^{0.5}=(...)\sqrt{(...)}.

    So the next stage is:
    =\frac{-3(x+2)}{2(3x+1)\sqrt{3x+1}}+\frac{1}{\sqrt{3x+1}}
    OK. Now find the lowest common denominator, which is 2(3x+1)\sqrt{3x+1}. So, writing the second fraction with this denominator, we get:
    =\frac{-3(x+2)}{2(3x+1)\sqrt{3x+1}}+\frac{2(3x+1)}{2(3x+1)  \sqrt{3x+1}}
    Now combine the fractions over a single denominator and simplify:
    =\frac{-3(x+2)+2(3x+1)}{2(3x+1)\sqrt{3x+1}}

    =\frac{3x-4}{2(3x+1)\sqrt{3x+1}}
    which you can write as:
    =\frac{3x-4}{2(3x+1)^{1.5}}
    if you like.

    Grandad
    Hi, your workings looks alright and great!!!!!
    Last edited by Punch; February 12th 2010 at 03:31 AM.
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