In preparation for Lagrange's Interpolation Theorem, I'm curious to know why a rational function can be put in the following form.
Suppose $Q$ is a polynomial with distinct roots $a_1,\dots,a_n$, and let $P$ be a polynomial with $\deg(P)
In preparation for Lagrange's Interpolation Theorem, I'm curious to know why a rational function can be put in the following form.
Suppose $Q$ is a polynomial with distinct roots $a_1,\dots,a_n$, and let $P$ be a polynomial with $\deg(P)
Multiply through by $Q(x)$ and note that both sides are polynomials of degree less than $n$ agreeing at the $n$ points $x=a_i$.