How do you write the partial fraction decomposition of the rational expression $8 / [ ( x + 2 ) ( x^2 + 4 ) ]$ ?

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Answer 1 · 2016-05-21T01:56:43

$1/(x+2) + (2-x)/ (x^2+4)$

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Solve these three equations,

From 4A+2C=8 , A= $(2-C/2)$

From 2B+C=0, B= $-C/2$

Therefore, A+B=2-C=0, hence C=2, B=-1 and A= 1.

The partial fractions are therefore $1/(x+2) + (2-x)/ (x^2+4)$

How do you write the partial fraction decomposition of the rational expression 8 / [ ( x + 2 ) ( x^2 + 4 ) ]8 / [ ( x + 2 ) ( x^2 + 4 ) ]?