#readwise # Partial Fractions  ## Metadata - Author: [[brilliant.org]] - Full Title: Partial Fractions - URL: https://brilliant.org/wiki/partial-fractions/ ## Summary Partial fractions is a method to break down complex rational functions into simpler parts. This technique is helpful for solving integration problems. The process involves factoring the denominator and finding coefficients for the simpler fractions. Partial fraction decomposition can also handle repeated factors and irreducible quadratics. This article is the first in a series of articles on partial fractions. Here are the rest: - [[Partial Fractions - Linear Factors]] - [[Partial Fractions - Limit Method]] - [[Partial Fractions - Cover Up Rule]] ## Highlights Partial fraction decomposition is a technique used to write a [rational function](https://brilliant.org/wiki/rational-functions/) as the sum of simpler rational expressions. $\frac{2}{x^2 - 1} \Rightarrow \frac{1}{x - 1} - \frac{1}{x + 1}.$ Partial fraction decomposition is a useful technique for some [[Integration]] problems involving rational expressions. Partial fraction decomposition is also useful for evaluating [telescoping sums](https://brilliant.org/wiki/telescoping-series/). It is the basis for a proof of [[Readwise/Articles/Euler's Formula|Euler's Formula]] by finding the antiderivative of a rational expression in two different ways. ([View Highlight](https://read.readwise.io/read/01jfjy1dtgst3d1z8phm4y9w0h)) ^tf9v88 ---