How to find the partial fraction of (z^2-1)/((z+1) (z+2))

Mark Elliott

Mark Elliott

Open question

2022-08-18

How to find the partial fraction of z 2 1 ( z + 1 ) ( z + 2 ) ?
I tried the method of
z 2 1 ( z + 1 ) ( z + 2 ) = A ( z + 1 ) + B ( z + 2 )
but it didn't work. Why is this?

Answer & Explanation

Bridget Vang

Bridget Vang

Beginner2022-08-19Added 11 answers

As both denominator and numerator have the same degree, first divide the polynomials:
z 2 1 z 2 + 3 z + 2 = 1 3 z + 2 z 2 + 3 z + 1
and now do partial fractions on the second summand above.
imire37

imire37

Beginner2022-08-20Added 8 answers

your fraction is improper so first
z 2 1 = ( z 1 ) ( z + 1 )
then you have
z 2 1 ( z + 1 ) ( z + 2 ) = z 1 z + 2
and then at last
z 1 z + 2 = 1 3 z + 2

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