You are Here: Home >< Maths

# C4 ~ Partial Fractions, help please! watch

1. Ok, so have the following partial fraction:

X^2 + X + 1
(X-1)(X+1)(X^2 -1)

which is
A/(X+1) + B/(X-1) + (Cx + D)/(X^2 +1)

By putting x=1 and x=-1 in, can work out B=3/4 and A=-1/4, but then where do you go? Am I on the right tracks?

Any help would be much appreciated!
2. You need to compare coefficients. Have a look at the coefficients of x^2 and the non x terms. Hope that helps.
3. (Original post by Sushmeist)
X^2 + X + 1
(X-1)(X+1)(X^2 -1)

which is
A/(X+1) + B/(X-1) + (Cx + D)/(X^2 +1)
(x2+x+1)/((x-1)(x+1)(x2-1))
= A/(x+1) + B/(x-1) + (Cx + D)/(x2+1)
= A(x-1)(x2+1) + B(x+1)(x2+1) + (Cx+D)(x-1)(x+1)

Let (x=1) => 4B = 3, so B = 3/4
Let (x=-1) => A = -1/4
Let (x=0) => B-A-D = 1, so D = B-A-1 = D => 3/4+1/4-1 = 0
Let (x=2) => 5A+15B+6C = 7, so C = (7-5(-1/4)-15(3/4))/6 = -1/2

=> (x2+x+1)/((x-1)(x+1)(x2-1))
= -1/(4(x+1)) + 3/(4(x-1)) - x/(2(x2+1))
=> 3/(4(x-1)) - 1/(4(x+1)) - x/(2(x2+1))
4. The denominator factorises into (x+1)^2(x-1)^2, so wouldn't it be A/x+1 + B/(x+1)^2 + C/x-1 + D/(x-1)^2?

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 23, 2006
Today on TSR

Uni realities

### University open days

• University of Lincoln
Mini Open Day at the Brayford Campus Undergraduate
Wed, 19 Dec '18
• University of East Anglia
Fri, 4 Jan '19
• Bournemouth University
Wed, 9 Jan '19
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams