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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
    • one year ago
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    \[\frac{ 4x^2+23x+24 }{ x^2+5x+6 }\]

  2. marco26
    • one year ago
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    First you need to decompose the fraction using variables like A, B, etc.

  3. katielong
    • one year ago
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    Ax + B + C/(x+2) + D/(x+3) ?

  4. katielong
    • one year ago
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    @marco26 ?

  5. marco26
    • one year ago
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    \[\frac{ 4x ^{2}+23x+24 }{ (x+2)(x+3) }=\frac{ A }{ (x+2) }+\frac{ B }{ (x+3) }\] -> this is what you need to get when you decompose the fraction.

  6. katielong
    • one year ago
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    okay, but isn't a 'C' term needed because the denominator is to the same degree as the numerator?

  7. marco26
    • one year ago
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    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
    • one year ago
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    now it's right

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