How do I obtain this from the formula of the geometric progression (which I 'only' know as $1+q+q^2+...+q^{n-1} = \frac{1-q^n}{1-q}$)? $$\frac{x_1^p-x^p}{x_1^q-x^q} = \frac{x_1^{p-1}+x_1^{p-2}x+...+x^{p-1}}{x_1^{q-1}+x_1^{q-2}x+...+x^{q-1}}$$
Thank you for any help!
Hint: consider $q = x_1/x{}{}{}$.
$$\begin{align} 1+q+\dots + q^{n-1} &= 1+ x_1/x+\dots + ( x_1/x)^{n-1} \\&= \frac 1{x^{n-1}}\left[ x^{n-1} + x^{n-2}x_1 + \dots + x_1^{n-1} \right] \end{align} $$