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8x+23/(x+3)(x+2) partial fraction decomposition

User Rujmah
by
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1 Answer

3 votes

Answer:

1/(x+3)+7/(x+2)

Explanation:

I'm assuming the full numerator is (8x+23)... and by making that assumption I'm assumed the fraction was (8x+23)/[(x+3)(x+2)].

(8x+23)/[(x+3)(x+2)]=A/(x+3)+B/(x+2)

8x+23=A(x+2)+B(x+3) I multiply both sides by (x+3)(x+2)

Set x to -2 that gives -16+23=B so this means B=7

Set x to -3 instead that gives -24+23=A(-1) so this means A=1

So (8x+23)/[(x+3)(x+2)]=1/(x+3)+7/(x+2)

User Rajeev Das
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5.8k points