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P3 Algebra

Express as partial fractions:

1) (x^3 + 3x^2 - 2x - 5) / ((x - 1)^2)(x^2 + 2).

2) (x^3 - x^2 - 1) / (x)(x^2 + x + 1).

3) 3 / (x^3 + 1).

Answers:

1) 3/(x - 1) - 1/(x - 1)^2 + (3 - 2x)/(x^2 + 2).

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

3) 1/(x + 1) + (-x + 2)/(x^2 - x + 1).

Cheers :smile:

Reply 1

dvs

What are you having trouble with?

For the first one:
(x^3 + 3x^2 - 2x - 5) / ((x - 1)^2)(x^2 + 2) = A/(x-1) + B/(x-1)^2 + Cx+D/(x^2+2)
(x^3 + 3x^2 - 2x - 5) = A(x-1)(x^2+2) + B(x^2+2) + Cx+D(x-1)^2
First, set x=1. This'll give you B=-1. Second, equate the coefficients of x^3, x^2 and x, and equate the terms independant of x. This should give you 4 equations in A, C and D (you already have the value of B). Solve them simultaneously to get A=3, C=-2 and D=3.

The other two are done in basically the same way.