does anybody know how this came from?

thank you

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- Jan 30th 2013, 04:09 AMcxz7410123Factorising
does anybody know how this came from?

thank you - Jan 30th 2013, 05:46 AMShakarriRe: Factorising
They use the fact that 5! = 5* 4! and 4!= 4*3! to change 8!/(4!*4!) into 8!/(4!*(4*3!)) and 8!/(5!*3!) into 8!/((5*4!)*3!) to get 4!3! in the denominator of both quantities then factorise 8!/(4!3!)

- Jan 30th 2013, 08:21 AMpspssRe: Factorising
for multiplicatin instead of (×), ( . ) is used

8!/4!.4! + 8!/5!.3!

= 8!/4!.4! + 8!/4!.5.3!

= 8!/4![1/4! + 1/5.3!]

= 8!/4![1/3!.4 + 1/5.3!]

= 8!/4!.3![1/4 + 1/5]

---- - Jan 30th 2013, 03:09 PMProve ItRe: Factorising
Actually, a (.) is used as a decimal point, it's actually a centred dot, $\displaystyle \displaystyle \begin{align*} \cdot \end{align*} $ which is used for multiplication. Though a $\displaystyle \displaystyle \begin{align*} \times \end{align*} $ is also acceptable as long as it doesn't get mixed up with any $\displaystyle \displaystyle \begin{align*} x \end{align*} $ variables.

- Jan 30th 2013, 05:53 PMtopsquarkRe: Factorising
The solution has already been given, but I thought I'd rewrite it a bit:

$\displaystyle \frac{8!}{4! \cdot 4!} + \frac{8!}{5! \cdot 3!} = \frac{8!}{4! \cdot 3!} \left ( \frac{1}{1 \cdot 4} + \frac{1}{5 \cdot 1} \right )$

We have a forum that deals with how to write expressions. It's the LaTeX Help forum. It's pretty easy to learn the basics. :)

-Dan