Question

Which expression is the partial fraction decomposition of

Answer 1

(3x+7)?(x+2)^2

Answer 2

@jim_thompson5910

Answer 3

did you mean (3x+7)/(x+2)^2

Answer 4

yea

Answer 5

let me show you the answer list

Answer 6

3/x+2+1/(x+2)^2
2/x+2+1/(x+2)
3/x+2+2/(x+2)^2
3/x+2-1/(x+2)^2

Answer 7

lets get it

Answer 8

Refer to these rules if needed
http://tutorial.math.lamar.edu/Classes/Alg/PartialFractions.aspx
\[\Large \frac{3x+7}{(x+2)^2} = \frac{A}{x+2}+\frac{B}{(x+2)^2}\]
\[\Large \frac{3x+7}{(x+2)^2} = \frac{A(x+2)}{(x+2)(x+2)}+\frac{B}{(x+2)^2}\]
\[\Large \frac{3x+7}{(x+2)^2} = \frac{A(x+2)}{(x+2)^2}+\frac{B}{(x+2)^2}\]
\[\Large \frac{3x+7}{(x+2)^2} = \frac{A(x+2)+B}{(x+2)^2}\]
\[\Large \frac{3x+7}{(x+2)^2} = \frac{Ax+2A+B}{(x+2)^2}\]
We see that the Ax and 3x match up, so Ax = 3x leading to A = 3.

The 7 and 2A+B match up, so 7 = 2A+B. We know A = 3, so 7 = 2*3+B. Solve for B to get B = ???

Answer 9

2

Answer 10

@jim_thompson5910

Answer 11

my bad had to take out the trash

Answer 12

so it would be c?

Answer 13

B = 2 is false

Answer 14

so b has to equal 1

Answer 15

yeah B = 1

Answer 16

\[\Large \frac{3x+7}{(x+2)^2} = \frac{A}{x+2}+\frac{B}{(x+2)^2}\]

\[\Large \frac{3x+7}{(x+2)^2} = \frac{3}{x+2}+\frac{1}{(x+2)^2}\]

Answer 17

wolfram can you give it (if you ever want to check)

Answer 18

but I don't think that jim_thompson is ever wrong.....

Answer 19

just saying, that if you are sitting alone, and want to check the answer.

Answer 20

Yea I meant to try to wolfram

Answer 21

I use wolfram to check, so that helps me keep the winning streak going lol