MYTUTOR SUBJECT ANSWERS

276 views

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

Step 1:

When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator.

In our case we have that the power of quadratic equation in the numerator is equal to 2, while the power of the denominator is 

(x-1)(x-2) = x- 3x +2 

which is equal to 2 as well.

Step 2:

Now we devide the numerator by the denominator.

Using long division we get that

(3x2 - 3x - 2)/(x-1)(x-2) = 3 + (6x-8)/(x- 3x + 2)

Step 3:

The next step is express (6x-8)/(x- 3x + 2) as a partial fraction

(6x-8)/(x- 3x + 2) = (6x-8)/(x-1)(x-2) 

(6x-8)/(x-1)(x-2) = A/x-1 + B/x-2

Step 4:

Now we multiply both the LHS and the RHS by (x-1)(x-2) because this leads to a common denominator.

6x - 8 = A(x-2) + B(x-1)

Now we have to use two different values for x, such that in the first instance B=0, and in the second instance,  A=0

Hence, when x=1,

6(1) - 8 = A(1-2) + B(1-1)

6 - 8 = -A + 0

-2 = - A

A = 2

When x=2

6(2) - 8 = A(2-2) + B(2-1)

12 - 8 = 0 + B

B = 4

Step 5:

Now going back to our original equation,

(3x2 - 3x - 2)/(x-1)(x-2) = 3 + (6x-8)/(x- 3x + 2)

 3 + (6x-8)/(x- 3x + 2) = 3 +  A/x-1 + B/x-2

and using A=2 , B=4 we get

3 + (6x-8)/(x- 3x + 2) = 3 +  2/x-1 + 4/x-2

Hence, our desired result is

(3x2 - 3x - 2)/(x-1)(x-2) =  3 +  2/x-1 + 4/x-2

Pantelis K. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor

7 months ago

Answered by Pantelis, an A Level Maths tutor with MyTutor


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

182 SUBJECT SPECIALISTS

£20 /hr

Alicia E.

Degree: Classics BA (Bachelors) - Exeter University

Subjects offered: Maths, Latin+ 2 more

Maths
Latin
English Literature

“Hello! My name is Alicia, most people just call me Alice, I'm happy with either. I am studying Classics at the University of Exeter so I am very much committed to the classical world but still enjoy the subjects I took at A-Level and ...”

£20 /hr

Peter W.

Degree: Aerospace Engineering (Masters) - Queen's, Belfast University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Second year Aerospace Engineering student at Queen's University Belfast. Happy to offer help in Maths, Further Maths and Physics at GCSE and A-Level, which I have great experience in both learning and tutoring.”

£20 /hr

Adam T.

Degree: Physics (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics

Maths
Physics

“About Me I am currently studying Mathematical Physics at the University of Edinburgh.  I find physics and maths interesting and exciting and I hope I can show you how intriguing and entertaining your course can be as well.   When stu...”

MyTutor guarantee

About the author

Pantelis K.

Currently unavailable: for regular students

Degree: MSci Mathematics (Masters) - University College London University

Subjects offered: Maths, Physics

Maths
Physics

“About Me Hi! My name is Pantelis and I am a 4th year student at University College London, in my favorite subject which is Mathematics. Having already faced the problems of not understanding what the lecturer means, feeling shy to a...”

MyTutor guarantee

You may also like...

Posts by Pantelis

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

Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Suppose you are given a rectangle where the length is equal to 2x+4 and its width is equal to 3x-2. Assuming that the perimeter is equal to 54 cm, what's the value of x?

Other A Level Maths questions

Find the roots of the equation y=x^2-8x+5 by completing the square.

How do I integrate ln(x)

What is the derivative of ln(x)?

What is dot product and how to calculate it?

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