## katieb 5 years ago What is the partial fraction decomposition? Please help me. These are impossible. :( -5x-15/(x+5)^2

1. anonymous

You have a repeated linear factor in the denominator, so you decompose the fraction as such:$\frac{-5x-15}{(x+5)^2}=\frac{A}{x+5}+\frac{B}{(x+5)^2}$You then multiply both sides by (x+5)^2 to obtain$-5x-15=A(x+5)+B$Expand and collect like terms:$-5x-15=Ax+(5A+B)$In order for this to be true, we must have$A=-5$(identifying it with the coefficient of x on the left) and $5A+B=-15$Since A has to be -5, we may solve for B:$-15=5A+B=5(-5)+B=-25+B \rightarrow B=-15+25=10$So A = -5 and B = 10, and your decomposition is$\frac{-5x-15}{(x+5)^2}=-\frac{5}{x+5}+\frac{10}{(x+5)^2}$

2. anonymous

You can always check by cross-multiplying the right-hand side to see if it gets you back to what you had originally.

3. KatieB

it's saying that's incorrect. :(

4. anonymous

Sorry, Katie, but the answer is correct. I've double-checked. Maybe you've entered something wrong?

5. KatieB

6. KatieB

Done.

7. KatieB

partial decomposition of... x^3+x^2-5/(x^2+7)^2

8. anonymous

9. KatieB

What is the partial fraction decomposition? 8x^2+20x+77/x(x-9)(x-8)

10. KatieB

Last one please and thank you so much, but it's due in 8 minutes.

11. anonymous

I can give you what I got, but I've rushed and can't guarantee. $\frac{77/72}{x}+\frac{60535/616}{x-9}-\frac{63299/693}{x-8}$

12. anonymous

wait

13. anonymous

-749/8 for the x-8 one 905/9 for x-9 one 77/72 for x one

14. KatieB

aw man too late

15. KatieB

thank you so much for trying! you're awesome!

16. anonymous

oh well...next time, don't leave it to the last minute! :p

17. anonymous

Go to khanacademy.org or YouTube if you need to see how partial fraction decomposition is done :)

18. KatieB

thank you!