Question

Consider the decomposition (x^2 + 3x - 5)/(x+1)(x^2+2) into partial fractions.

Answer 1

\[\frac{x^2+3 x-5}{(x+1) \left(x^2+2\right)}=\frac{10 x-1}{3 \left(x^2+2\right)}-\frac{7}{3 (x+1)}
\]

Answer 2

wow, that was quick...

Answer 3

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

Answer 4

I agree, wow that was quick. How did you get to the solution so quick? Please explain thanks

Answer 5

wolfram works nicely.
otherwise you have to solve a system of equations for this one

Answer 6

\[\frac{x^2+3 x-5}{(x+1) \left(x^2+2\right)}=\frac{a x+b}{ x^2+2}+\frac{c}{x+1}\]

Answer 7

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

Answer 8

\[x^2+3x-5=(ax+b)(x+1)+c(x^2+2)\]

Answer 9

replace x by -1 finds c right away you get \(-7=3c\) so \(c=-\frac{7}{3}\)

Answer 10

the rest is annoying

Answer 11

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 \[ A= -\frac 13, B= \frac {10}3\]

Answer 12

The above method is called the cover-up method. It is fast.

Answer 13

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
\[\frac{(-1)^2+3 (-1)-5}{(-1)^2+2}=\frac{(1-1) (A x+B)}{x^2+2}+C
\]
\[\frac{-7}3=0+C
\]

Answer 14

yes, this is a much snappier method than system of equations, if you are familiar with complex numbers

Answer 15

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.

Answer 16

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.

Answer 17

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?

Answer 18

Practice on
http://saab.org and be sure to like us on Facebook

Answer 19

Excellent, thanks so much