# Thread: Dividing three fractions

1. ## 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

2. Originally Posted by Fnus
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
$\displaystyle \frac{ \frac{b^{n + 1}n - a^{n + 1}n}{n + 1} }{ \frac{b^{n + 1} - a^{n + 1}}{n + 1} }$

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

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

$\displaystyle = n$

-Dan

3. Hello,

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

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

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

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

And just continue...

4. Well, if I was going to continue, I'd just cancel the two $\displaystyle \frac{\pi}{N}$, but that can't be right >.<

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

5. Originally Posted by Fnus
Well, if I was going to continue, I'd just cancel the two $\displaystyle \frac{\pi}{N}$, but that can't be right >.<

$\displaystyle =\frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}}$
Multiply the top and bottom by N:
$\displaystyle \frac{\frac{\pi}{N}-\pi}{\frac{\pi}{N}} \cdot \frac{N}{N}$

What does this give you?

-Dan

6. Originally Posted by Moo
Hello,

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

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

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

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

And just continue...

A little mistake, in red...

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