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## katielong one year ago express: (4x^2+23x+24)/(x^2+5x+6) in partial fractions

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1. katielong

$\frac{ 4x^2+23x+24 }{ x^2+5x+6 }$

2. marco26

First you need to decompose the fraction using variables like A, B, etc.

3. katielong

Ax + B + C/(x+2) + D/(x+3) ?

4. katielong

@marco26 ?

5. marco26

$\frac{ 4x ^{2}+23x+24 }{ (x+2)(x+3) }=\frac{ A }{ (x+2) }+\frac{ B }{ (x+3) }$ -> this is what you need to get when you decompose the fraction.

6. katielong

okay, but isn't a 'C' term needed because the denominator is to the same degree as the numerator?

7. marco26

Sorry I was wrong. With the same degree you have to do long division first. Divide the numerator with the denominator and you should get $\frac{ 4x ^{2} +23x+24}{ x ^{2}+5x+6 }=4+\frac{ 3x }{ x ^{2}+5x+6 }$ and proceed to decomposition.

8. anonymous

now it's right

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