Home > Homework Forum

Partial fractions homework help!

pewpew
17 Feb 09, 22:04

Hello, I really need some help with some questions in my Partial Fractions homework..

6.           x
       ----------------

        (1-x^2)(x-1)

9.          2x^3

     ----------------------

       (1+x^2)(1-x)^2

10.   x^2 + 3x
       ---------------

        x^2 - 4

11.      x^3 - x^2 - 4
         --------------------
         x^2 - 1

I need to express these as partial fractions..
16/f/lonely
17 Feb 09, 22:05

Whats the question?
Only-Way-4-Destiny!
17 Feb 09, 22:06

Find x?
16/f/lonely
17 Feb 09, 22:07

Har? How to find x when no opposite side????
Only-Way-4-Destiny!
17 Feb 09, 22:09

he wana simplify them?
pewpew
17 Feb 09, 22:18

i did the easier questions.. must use the formula mah.. they just want me to express them as partial fractions.
eagle
17 Feb 09, 22:25

pple... express it as partial fractions...

i.e. first question

$\frac{x}{\left (1-x^{2} \right )\left (x-1 \right )}$

$=\frac{x}{\left (1-x \right )(1+x)\left (x-1 \right )}$

$=-\frac{x}{\left (1-x \right )^{2}(1+x)}$

$=\frac{1}{4}\left (\frac{1}{1+x} \right )+\frac{1}{4}\left (\frac{1}{1-x} \right )-\frac{1}{2}\frac{1}{(1-x)^{2}}$

Try the rest guys :D
16/f/lonely
17 Feb 09, 22:38

Ohhh...that.

I'm getting too rusty.
pewpew
17 Feb 09, 22:43

huh? how did u suddenly get 1/4 and 1/2? sub what and what? i seem to be getting it wrong..
tinuviel07
17 Feb 09, 22:45

either, you split into A & B then multiply denominator, or you compare coefficient... or what's the other method huh.. forgot
pewpew
17 Feb 09, 22:58

ahh.. damn im so screwed.
xstryker
17 Feb 09, 23:00

hooray

2 weeks due hw for pewpew
eagle
17 Feb 09, 23:03

Originally posted by pewpew:

huh? how did u suddenly get 1/4 and 1/2? sub what and what? i seem to be getting it wrong..

hmm.... i skipped a few steps...

One fool proof way is to do

A/(1+x) + B/(1-x) + C/(1-x)^2

then solve the coefficients
wee_ws
18 Feb 09, 19:22

Hi,

For Q10 & Q11, the rational expression is improper. You need to use long division or algebraic manipulation before finding partial fractions.

By algebraic manipulation, the numerator in Q10 may be written as (x^2 - 4) + 3x + 4.

In addition, note the following pointers:

1. Can the denominator be factorised? For example, x^2 - 1 = (x - 1)(x + 1).

2. Recall the three decomposition rules which can be found in the formulae booklet, which will accompany you for all tests and examinations:

(i) linear factors,

(ii) repeated linear factors,

(iii) quadratic non-factorisable factors (e.g. x^2 + 1).

3. Use of the cover-up method to find constants, or comparing coefficients of x, x^2, etc.

Thanks!

Cheers,
Wen Shih