MYTUTOR SUBJECT ANSWERS

1050 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

1 year ago

Answered by Pantelis, an A Level Maths tutor with MyTutor


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

330 SUBJECT SPECIALISTS

£20 /hr

Mabast H.

Degree: Physics (Bachelors) - Imperial College London University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
Chemistry
-Personal Statements-

“Undergraduate Physicist with lots of experience in teaching in different fields and age groups, looking to instil a passion for learning into students.”

MyTutor guarantee

£20 /hr

John W.

Degree: Mathematics (Masters) - St. Andrews University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I've done a broad range of maths learning and tutoring over the years, now continuing this on to university I'm sure I'll be able to help you out!”

£36 /hr

Henri F.

Degree: Aerospace Engineering PhD Spacecraft Control (Doctorate) - Bristol University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
Further Mathematics
Extended Project Qualification
.STEP.
.PAT.

“Aerospace Engineering PhD candidate in spacecraft control with 7 years of experience in tutoring.”

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

How do I differentiate f(x) = cos(x)/x?

Find the first differential with respect to x of y=tan(x)

The quadratic equation 2x^2+ 6x+7 has roots a and b. Write down the value of a+b and the value of ab.

What is the chain rule and how does it work?

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