MYTUTOR SUBJECT ANSWERS

106 views

What are the rules for decomposition of partial fractions?

There are some very useful rules when dealing with partial fractions

1) 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).

Filip W. 13 Plus  Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor,...

3 months ago

Answered by Filip, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

183 SUBJECT SPECIALISTS

£20 /hr

George B.

Degree: Physics with Industrial experience (Masters) - Bristol University

Subjects offered: Maths, Physics

Maths
Physics

“Myself: I'm a Physics student at the University of Bristol. My passion is Physics and Maths. I think any theory can be made interesting and exciting. My tutorials will shows my informative and passionate nature.  I have numerous expe...”

£20 /hr

Shandon W.

Degree: Combined Honours in Social Sciences (Economics, Spanish) (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 2 more

Maths
Spanish
Economics
Chemistry

“I am currently a second year student at the University of Durham, studying Economics and Spanish. I have always found it easy to take on difficult concepts, and I hope to be able to pass on this understanding to other students. Having...”

MyTutor guarantee

£20 /hr

Lewis M.

Degree: Biology (Masters) - Bristol University

Subjects offered: Maths, Biology

Maths
Biology

“About Me: I am a Biology student at Bristol University. I have always loved science and maths and I hope this will come across in my sessions! I have been invloved with tutoring for the majority of my school life, taking time out of ...”

About the author

Filip W.

Currently unavailable: for new students

Degree: MSci Chemical Physics (Masters) - Bristol University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“My name is Filip and I'm a 3rd year student of Chemical Physics at Bristol Uni. I'm quite chatty, friendly and find science really exciting! I'm sure I'd be able to convince you that science can be fun ;)! Relevant experience I have a...”

You may also like...

Posts by Filip

Resolving the forces for an object suspended on two strings.

What are the rules for decomposition of partial fractions?

What is dot product and how to calculate it?

Other A Level Maths questions

Express (2x-1)/(x-1)(2x-3) in partial fractions.

Differentiation: How to use the chain rule

The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

What is the difference between definite and indefinite integrals?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok