Didee
  • Didee
Consider the decomposition (x^2 + 3x - 5)/(x+1)(x^2+2) into partial fractions.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[\frac{x^2+3 x-5}{(x+1) \left(x^2+2\right)}=\frac{10 x-1}{3 \left(x^2+2\right)}-\frac{7}{3 (x+1)} \]
anonymous
  • anonymous
wow, that was quick...
lgbasallote
  • lgbasallote
hmm good answer @eliasaab..though it would be appreciated if you posted some solutions. other users who have the same problems might wanna have some references. and also for the asker to find where his/her solution went wrong yes? thanks :DDD

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Didee
  • Didee
I agree, wow that was quick. How did you get to the solution so quick? Please explain thanks
anonymous
  • anonymous
wolfram works nicely. otherwise you have to solve a system of equations for this one
anonymous
  • anonymous
\[\frac{x^2+3 x-5}{(x+1) \left(x^2+2\right)}=\frac{a x+b}{ x^2+2}+\frac{c}{x+1}\]
anonymous
  • anonymous
Write \[\frac{x^2+3 x-5}{(x+1) \left(x^2+2\right)}= \frac{A x+B}{x^2+2}+\frac{C}{x+1} \] Then find A, B, C
anonymous
  • anonymous
\[x^2+3x-5=(ax+b)(x+1)+c(x^2+2)\]
anonymous
  • anonymous
replace x by -1 finds c right away you get \(-7=3c\) so \(c=-\frac{7}{3}\)
anonymous
  • anonymous
the rest is annoying
anonymous
  • anonymous
To find Multiply the two sides by (x+1) and let x = -1 You get \[ C=- \frac 7 3\] Multiply the two sides (original) by (x^2 +1) and put x=i, you can compute A, B together and you get \[ A= -\frac 13, B= \frac {10}3\]
anonymous
  • anonymous
The above method is called the cover-up method. It is fast.
anonymous
  • anonymous
Let me try to tell you how you get C. Multiply the two sides by (x+1) you get \[\frac{x^2+3 x-5}{x^2+2}=\frac{(x+1) (A x+B)}{x^2+2}+C \] if you put x =-1, you get \[\frac{(-1)^2+3 (-1)-5}{(-1)^2+2}=\frac{(1-1) (A x+B)}{x^2+2}+C \] \[\frac{-7}3=0+C \]
anonymous
  • anonymous
yes, this is a much snappier method than system of equations, if you are familiar with complex numbers
Didee
  • Didee
thanks guys, my textbook gives some long calculation. Would appreciate if you can post which website is good for more of these examples and solution as per your method.
anonymous
  • anonymous
You can use my site. Please use Firefox to access http://moltest.missouri.edu/mucgi-bin/calculus.cgi Choose Calc II (Techniques of Integration) to practice problems similar to the attached file and others. Where the parameters changes form test to test and complete solutions are given.
Didee
  • Didee
Thanks so much. This module is killing me. I've attached a previous exam paper and struggle with these problems. Will I get more examples with solutions on these also on that website?
anonymous
  • anonymous
Practice on http://saab.org and be sure to like us on Facebook
Didee
  • Didee
Excellent, thanks so much

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