express: (4x^2+23x+24)/(x^2+5x+6) in partial fractions

Question

katielong · Answer

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

marco26 · Answer

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

katielong · Answer

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

katielong · Answer

@marco26 ?

marco26 · Answer

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

katielong · Answer

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

marco26 · Answer

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.

anonymous · Answer

now it's right