What are the rules for decomposition of partial fractions?

There are some very useful rules when dealing with partial fractions1) For every linear factor such as ax + b in the denominator, there will be a partial fraction of the form A / ax + b. 2)  For every repeated factor such as (ax + b)2 in the denominator, there will be two partial fractions: A/ ax + b and B/ (ax + b)2  . For higher powers there will be correspondingly more terms. 3) For quadratic factors in the denominator e.g. ax2 + bx + c there will be a partial fraction of the form: Ax + B / ax2 + bx +c.For example, let's decompose (7x + 2) / [(x + 2)^2 * (x - 2)]. Using the rules above, (x + 2)^2 would give us A / (x + 2) + B / (x+2)^2. (x - 2) in the denominator would give C / (x - 2). Therefore, the partial fraction (7x + 2) / [(x + 2)^2 * (x - 2)] can also be written in the form: A / (x + 2) + B / (x+2)^2 +  C / (x - 2).In fact, having equated appropriate coefficients we find out that: (7x + 2) / [(x + 2)^2 * (x - 2)] = - 1/ (x + 2) + 3 / (x+2)^2 + 1 / (x - 2).

FW
Answered by Filip W. Maths tutor

7703 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the following equation for k, giving your answers to 4 decimal places where necessary: 3tan(k)-1=sec^2(k)


The curve C has the equation: 2(x^2)y + 2x + 4y – cos (πy) = 17 use implicit differentiation to find dy/dx in terms of x and y


f(x) = x^3 - 13x^2 + 55x - 75 , find the gradient of the tangent at x=3


Sketch the graphs of y = f(x), y = g(x) and find the point(s) where f and g intersect.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning