Question

PLZ HELP THANKS!
Find the partial fraction decomposition for the rational expression.
8x+236
OVER
(x+7)(x+2)(x+13)

Answer 1

you want the snap way?

Answer 2

ha i dont know the best way i ges

Answer 3

best way is snap way. write it down nice and large. you want to know what number goes over the factor (x+7)

Answer 4

x + 7 = 0 means x = -7

Answer 5

put replace x everywhere you see it by -7, but ignore the factor of x + 7 in the denominator

Answer 6

o ok

Answer 7

get
\[\frac{8\times -7+236}{(-7+2)(-7+13)}\]

Answer 8

this is what goes over the x + 7 term

Answer 9

is that the final answer?

Answer 10

oh no

Answer 11

that is just A here
\[\frac{A}{x+7}\]

Answer 12

so we just found a now we plug that in for?

Answer 13

yup that is A

Answer 14

lets make sure it is clear what the goal is. you want to write
\[\frac{8x+263}{(x+7)(x+2)(x+13)}=\frac{A}{x+7}+\frac{B}{x+2}+\frac{C}{x+13}\]

Answer 15

so your job is finding A, B, and C

Answer 16

ok

Answer 17

so we can find A as i said. put your hand over the x+7 part and just replace x everywhere by -7

Answer 18

then how i find the others?

Answer 19

did you get -6?

Answer 20

or did i mess up?

Answer 21

o I was not woorking it I was just trying to get how to then was going to do the whole thing

Answer 22

maybe it is -36 by calculator is off

Answer 23

so how would i find the others after i find a?
haha

Answer 24

ok lets assume we can do it. the computation is
\[\frac{-7\times 8+236}{(-7+2)(-7+13)}\]

Answer 25

we do the others exactly the same way

Answer 26

we want to know what goes over x+2

Answer 27

x+2 = 0 means x = -2. put your hand over that factor and then replace all x's by -2

Answer 28

o ok!

Answer 29

the computation is
\[\frac{8\times -2+236}{(-2+7)(-2+13)}\]

Answer 30

and for the third guess what?

Answer 31

\[\frac{8\times -13+236}{(-13+7)(-13+2)}\]

Answer 32

first one goes over x+7
second goes over x+2
third goes over x+13

Answer 33

apparently i am too stupid to actually calculate these numbers but they are the ones you want

Answer 34

i will try them, let me know what you get

Answer 35

then we can write the "final answer"

Answer 36

ha ok ok, let me see if i got this you take one x value from bottom and find x then plug it in to ever x in the problem and do that with all of them then you have three problems and do you solve thos and how?

Answer 37

then you are done. you need to find A, B and C

Answer 38

then just write the answer.

Answer 39

\[A=\frac{8\times (-7)+236}{(-7+2)(-7+13)}\]

Answer 40

whatever that number is, that is A the number that goes over x + 7

Answer 41

if i had a better calculator i could compute it quickly.

Answer 42

how do i do it without calculator or really bad calculator?

Answer 43

well -8*7=-56

Answer 44

236-56=180

Answer 45

numerator is 180

Answer 46

(-7+2)(-7+13)=-5*-5=25

Answer 47

and 180/25=36/5

Answer 48

i guess. did i do it right?

Answer 49

no i didn't

Answer 50

(-7+2)(-7+13)=-5*6=-30

Answer 51

180/-30=-6

Answer 52

so A = -6 and one term will be
\[\frac{-6}{x+7}\]

Answer 53

\[B=\frac{8\times(-2)+236}{(-2+7)(-2+13)}\]

Answer 54

what will the last term be over 13?

Answer 55

the last one will be over x+13

Answer 56

yes and that is c?

Answer 57

yes C

Answer 58

we didn't compute it yet

Answer 59

did you get B?

Answer 60

could we

Answer 61

i wrote it above, do you see it? i just didn't compute it yet

Answer 62

no this one looks harder then i will do b

Answer 63

ok let me know what you get and i will check it

Answer 64

i got a number for C

Answer 65

ha not yet

Answer 66

4/x+2

Answer 67

use a calculator it is easier that way

Answer 68

oh that is B i didn't compute that one hold on

Answer 69

i computed C

Answer 70

ya wht u get

Answer 71

2

Answer 72

positive>?

Answer 73

i did get 4 for B yes

Answer 74

yes i got positive 2

Answer 75

ok thanks!

Answer 76

i may need help later to

Answer 77

welcome. hope method is clear. they get harder.

Answer 78

crap haha