5 1 Partial Fractions Intro – Class 11TH Math

Introduction

We have learnt how to add rational fractions into a single fraction. For example:

\dfrac{1}{x-1} + \dfrac{2}{x+2} = \dfrac{3x}{(x-1)(x+2)}

\dfrac{2}{x+1} + \dfrac{1}{(x+1)^2} + \dfrac{3}{x-2} = \dfrac{5x^2 + 5x - 3}{(x+1)^2(x-2)}

In this unit we reverse that process: express a single rational fraction as a sum of simpler fractions called partial fractions. This is called partial fraction resolution, a valuable tool in calculus.

An open sentence using $=$ is an equation.

Conditional equation: true only for particular values (e.g. $2x = 3$ when $x = \dfrac{3}{2}$ ).
Identity: true for all values of the variable (e.g. $(x+3)(x+4) = x^2 + 7x + 12$ ).

The symbol $\equiv$ may be used for both equation and identity.

Introduction

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