Title: 3_6 Partial Fractions
Course: HELM Workbooks 2023-2024 > Section: HELM 3: Equations, Inequalities and Partial Fractions

Introduction

It is often helpful to break down a complicated algebraic fraction into a sum of simpler fractions. For example it can be shown that \[\dfrac{4x+7}{x^2+3x+2}\] has the same value as \[\dfrac{1}{x+2} +\dfrac{3}{x+1}\] for any value of \(x\). We say that \( \dfrac{4x+7}{ x^2+3x+2}\) is identically equal to \(\dfrac{1}{ x+2} + \dfrac{3}{ x+1}\) and that the partial fractions of \(\dfrac{4x+7}{ x^2+3x+2}\) are \(\dfrac{1}{ x+2}\) and \(\dfrac{3}{ x+1}\). The ability to express a fraction as its partial fractions is particularly useful in the study of Laplace transforms, \(Z\)-transforms, Control Theory and Integration. In this Section we explain how partial fractions are found.