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express 1/(x+1)(x+2) as partial fractions

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user4825270 | Student | eNoter

Posted September 7, 2013 at 11:48 AM via web

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express 1/(x+1)(x+2) as partial fractions

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llltkl | College Teacher | Valedictorian

Posted September 7, 2013 at 12:54 PM (Answer #1)

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To express `1/((x+1)(x+2))` as partial fractions

Observe that the factors in the denominator are `(x+1)` and `(x+2)` . So, we can write:

`1/((x+1)(x+2))=A/(x+1)+B/(x+2)` where `A` and `B` are numbers.

We multiply both sides by the common denominator `(x+1)(x+2)` :

`1=A(x+2)+B(x+1)`

Note: if `x=-2, B=-1`

if `x=-1, A=1`

Putting these results together we have:

`1/((x+1)(x+2))=1/(x+1)+((-1))/(x+2)`

`=1/(x+1)-1/(x+2)` and we have expressed the given fraction in partial fractions.

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