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Math Help - Dividing three fractions

  1. #1
    Junior Member Fnus's Avatar
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    Dividing three fractions

    I have three fractions, and I need to divide them, but , I don't even know where to begin!

    The first one is supposed to give me n, but I get it to give me 2n, so I gave up.
    I think the second one is supposed to give me 2n, and the third supposed to give me n/2, but I'm not sure.

    Can anyone help me step by step, maybe?

    Thanks a ton
    Attached Thumbnails Attached Thumbnails Dividing three fractions-1.jpg   Dividing three fractions-2.jpg   Dividing three fractions-3.jpg  
    Last edited by topsquark; April 21st 2008 at 02:54 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Fnus View Post
    I have three fractions, and I need to divide them, but , I don't even know where to begin!

    The first one is supposed to give me n, but I get it to give me 2n, so I gave up.
    I think the second one is supposed to give me 2n, and the third supposed to give me n/2, but I'm not sure.

    Can anyone help me step by step, maybe?

    Thanks a ton
    The first one is
    \frac{ \frac{b^{n + 1}n - a^{n + 1}n}{n + 1} }{ \frac{b^{n + 1} - a^{n + 1}}{n + 1} }

    = \frac{b^{n + 1}n - a^{n + 1}n}{b^{n + 1} - a^{n + 1}}

    = \frac{\left ( b^{n + 1} - a^{n + 1} \right ) n}{b^{n + 1} - a^{n + 1}}

    = n

    -Dan
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  3. #3
    Moo
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    Hello,

    For the second one, let N be 2n+1 (it'd be too much to copy it each time...)

    \frac{\color{blue}a^N(\frac{\pi}{N}-\pi)+b^N(\pi-\frac{\pi}{N})}{\color{red} \frac{\pi b^N}{N}-\frac{\pi a^N}{N}}

    =\frac{(\frac{\pi}{N}-\pi)({\color{blue} a^N-b^N})}{\frac{\pi}{N}({\color{blue} a^N-b^n})}

    =\frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}}

    And just continue...
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  4. #4
    Junior Member Fnus's Avatar
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    Well, if I was going to continue, I'd just cancel the two \frac{\pi}{N}, but that can't be right >.<

    <br />
=\frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}}<br />
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Fnus View Post
    Well, if I was going to continue, I'd just cancel the two \frac{\pi}{N}, but that can't be right >.<

    <br />
=\frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}}<br />
    Multiply the top and bottom by N:
    \frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}} \cdot \frac{N}{N}<br />

    What does this give you?

    -Dan
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  6. #6
    Moo
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    Quote Originally Posted by Moo View Post
    Hello,

    For the second one, let N be 2n+1 (it'd be too much to copy it each time...)

    \frac{\color{blue}a^N(\frac{\pi}{N}-\pi)+b^N(\pi-\frac{\pi}{N})}{\frac{\pi b^N}{N}-\frac{\pi a^N}{N}}

    =\frac{(\frac{\pi}{N}-\pi)({\color{blue} a^N-b^N})}{{\color{red} - } \frac{\pi}{N}({\color{blue} a^N-b^N})}

    =\frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}}

    And just continue...

    A little mistake, in red...

    So it's \frac{\pi-\frac{\pi}{N}}{\frac{\pi}{N}}
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