# Math Help - Simplifying Expression with Like Denominators and Factorials

1. ## Simplifying Expression with Like Denominators and Factorials

Hi,

I am having difficulties simplifying the expression $\frac{1}{k!}-\frac{1}{(k+1)!}$.

To obtain like denominators, $\frac{1}{k!}-\frac{1}{(k+1)!}=\frac{(k+1)!-k!}{k!(k+1)!}$, but I do not know how to further simplify the expression. The factorials are messing with me, I think.

Any help would be most certainly appreciated!

Cheers!

3. ## Re: Simplifying Expression with Like Denominators and Factorials

Hello, SC313!

$\text{Simplify: }\:\frac{1}{k!}-\frac{1}{(k+1)!}$

Multiply the first fraction by $\frac{k+1}{k+1}$

. . $\frac{1}{k!}\cdot\frac{k+1}{k+1} - \frac{1}{(k+1)!} \;=\;\frac{k+1}{(k+1)!} - \frac{1}{(k+1)!} \;=\;\frac{(k+1) - 1}{(k+1)!} \;=\;\frac{k}{(k+1)!}$