katielong
  • katielong
express: (4x^2+23x+24)/(x^2+5x+6) in partial fractions
Mathematics
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katielong
  • katielong
express: (4x^2+23x+24)/(x^2+5x+6) in partial fractions
Mathematics
jamiebookeater
  • jamiebookeater
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katielong
  • katielong
\[\frac{ 4x^2+23x+24 }{ x^2+5x+6 }\]
marco26
  • marco26
First you need to decompose the fraction using variables like A, B, etc.
katielong
  • katielong
Ax + B + C/(x+2) + D/(x+3) ?

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katielong
  • katielong
marco26
  • 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.
katielong
  • katielong
okay, but isn't a 'C' term needed because the denominator is to the same degree as the numerator?
marco26
  • 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.
anonymous
  • anonymous
now it's right

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