Simplifying $\frac{x^6-1}{x-1}$ I have this:
$$\frac{x^6-1}{x-1}$$
I know it can be simplified to $1 + x + x^2 + x^3 + x^4 + x^5$
Edit : I was wondering how to do this if I didn't know that it was the same as that.

Just apply the following reduction formula inductively.

$$\frac{x^n-1}{x-1} = x^{n-1}+\frac{x^{n-1}-1}{x-1}$$

Derivation
$$\begin{array}{lll}
\frac{x^n-1}{x-1}&=&\frac{x^n - x^{n-1}+x^{n-1}-1}{x-1}\\
&=&\frac{x^n - x^{n-1}+x^{n-1}-1}{x-1}\\
&=&\frac{x^{n-1}(x-1)+x^{n-1}-1}{x-1}\\
&=&x^{n-1}+\frac{x^{n-1}-1}{x-1}\\
\end{array}$$
