Defiance
  • Defiance
Will medal... 2x-9/x^2- x- 6 = A/x-3 + B/x+2 / as in fraction and ^2 as squared
Mathematics
chestercat
  • chestercat
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
partial fractions?
Defiance
  • Defiance
Mhm.

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Defiance
  • Defiance
Defiance
  • Defiance
Hello.?
Defiance
  • Defiance
Ganeshie8, can you help?
ganeshie8
  • ganeshie8
you may use the cover up method http://www.math-cs.gordon.edu/courses/ma225/handouts/heavyside.pdf
ganeshie8
  • ganeshie8
\[\dfrac{2x-9}{x^2- x- 6} = \dfrac{A}{x-3} + \dfrac{B}{x+2} \] \[\dfrac{2x-9}{(x-3)(x+2)} = \dfrac{A}{x-3} + \dfrac{B}{x+2} \]
ganeshie8
  • ganeshie8
Look at the "left hand side" expression. Cover up \(x-3\) and plugin \(x=3\), what do you get ?
ganeshie8
  • ganeshie8
\[\dfrac{2x-9}{(x+2)} \] plugin x=3 above
Defiance
  • Defiance
2(3)-9/5
Defiance
  • Defiance
So, 1 / 5?
ganeshie8
  • ganeshie8
(2(3)-9)/5 (6-9)/5 = ?
Defiance
  • Defiance
1/5 and -3/5
ganeshie8
  • ganeshie8
what 1/5 ?
Defiance
  • Defiance
Wait sorry.
Defiance
  • Defiance
i get -3/5 on both
ganeshie8
  • ganeshie8
Lets work it step by step, shall we ? so far we have \(A=-\dfrac{3}{5}\)
Defiance
  • Defiance
Yes.
ganeshie8
  • ganeshie8
Next, cover up \(x+2\) and plugin \(x=-2\) in : \[\dfrac{2x-9}{(x-3)} \]
Defiance
  • Defiance
13/5?
ganeshie8
  • ganeshie8
Yep! you may double check with wolfram http://www.wolframalpha.com/input/?i=partial+fractions+%282x-9%29%2F%28x%5E2-+x-+6%29
Defiance
  • Defiance
Thanks so much!
ganeshie8
  • ganeshie8
yw

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