anonymous one year ago Will medal... 2x-9/x^2- x- 6 = A/x-3 + B/x+2 / as in fraction and ^2 as squared

1. misty1212

HI!!

2. misty1212

partial fractions?

3. anonymous

Mhm.

4. anonymous

@ganeshie8

5. anonymous

Hello.?

6. anonymous

Ganeshie8, can you help?

7. ganeshie8

you may use the cover up method http://www.math-cs.gordon.edu/courses/ma225/handouts/heavyside.pdf

8. ganeshie8

\[\dfrac{2x-9}{x^2- x- 6} = \dfrac{A}{x-3} + \dfrac{B}{x+2} \] \[\dfrac{2x-9}{(x-3)(x+2)} = \dfrac{A}{x-3} + \dfrac{B}{x+2} \]

9. ganeshie8

Look at the "left hand side" expression. Cover up \(x-3\) and plugin \(x=3\), what do you get ?

10. ganeshie8

\[\dfrac{2x-9}{(x+2)} \] plugin x=3 above

11. anonymous

2(3)-9/5

12. anonymous

So, 1 / 5?

13. ganeshie8

(2(3)-9)/5 (6-9)/5 = ?

14. anonymous

1/5 and -3/5

15. ganeshie8

what 1/5 ?

16. anonymous

Wait sorry.

17. anonymous

i get -3/5 on both

18. ganeshie8

Lets work it step by step, shall we ? so far we have \(A=-\dfrac{3}{5}\)

19. anonymous

Yes.

20. ganeshie8

Next, cover up \(x+2\) and plugin \(x=-2\) in : \[\dfrac{2x-9}{(x-3)} \]

21. anonymous

13/5?

22. 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

23. anonymous

Thanks so much!

24. ganeshie8

yw