Let $$ l_i(x)=\prod_{j=0,\ i\neq j}^n \frac{x-x_j}{x_i-x_j} $$ where $x_0,...x_n\in \mathbb{R}$ and $\forall_{i,j}\ i\neq j \implies x_i\neq x_j$
Show that: $$ \forall_{x\in \mathbb {R}}\ \sum_{i=0}^n l_i(x)=1 $$
I know how to do it when $x\in\{x_0,...,x_n\}$, but I don't know how to prove it for any $x$