Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

@marco26 ?

Answer 5

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

Answer 6

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

Answer 7

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.

Answer 8

now it's right