MYTUTOR SUBJECT ANSWERS

357 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,...

9 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

324 SUBJECT SPECIALISTS

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£24 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

Me V. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor
£20 /hr

Vaikkun V.

Degree: Electrical and Electronic Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I am passionate, motivated, and always hungry for more. I can bring energy and life to the classroom, and engage the student.”

MyTutor guarantee

About the author

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

Filip W.

Currently unavailable: for new students

Degree: MSci Chemical Physics (Masters) - Bristol University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
Biology

“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

A girl saves money over 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence. Find the amount she saves in Week 200. Calculate total savings over the 200 week period.

Differentiate 4x^2 + 2ln3x + e^x

y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

The region R is bounded by the curve y=sqrt(x)+5/sqrt(x) the x-axis and the lines x = 3, x = 4. Find the volume generated when R is rotated through four right-angles about the x-axis. Give your answer correct to the nearest integer.

View A Level Maths tutors

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

mtw:mercury1:status:ok