Question

calculus 2 - partial fractions

Answer 1

step1 : factor the denominator

Answer 2

x(x+6)

Answer 3

step2 : setup the fractions

\(\large \frac{x+1}{x(x+6)} = \frac{A}{x} + \frac{B}{x+6}\)

Answer 4

ok I understand that much

Answer 5

u need to find A and B

Answer 6

get rid of denominators

Answer 7

\(\large \frac{x+1}{x(x+6)} = \frac{A}{x} + \frac{B}{x+6}\)


multiply x(x+6) both sides

\(\large x+1 = A(x+6) + Bx\)

Answer 8

ok i got there

Answer 9

compare x coefficients and constant terms both sides

Answer 10

\(\large x + 1 = A(x+6) + Bx\)

x coefficient on left side = 1
x coefficient on right side = A + B

comparing :
\(A + B = 1\)

Answer 11

\(\large x + 1 = A(x+6) + Bx\)

constant term on left side = 1
constant term on right side = 6A

comparing :
\(6A = 1\)

Answer 12

this is where I'm lost

Answer 13

you divide x on both sides?

Answer 14

u have two equations and two unknowns, u can solve them

Answer 15

\(A+B = 1\)
\(6A = 1\)

Answer 16

solve them and find A, B values

Answer 17

constant term on left side = 1 constant term on right side = 6A comparing : 6A=1

Answer 18

I dont get this part

Answer 19

look at below :
\(\large x + 1 = A(x+6) + Bx\)

Answer 20

whats the constant term on left side ?

Answer 21

1

Answer 22

there is none?

Answer 23

yes, constant term on left sides is 1
whats the constant term on right side ?

Answer 24

remember : constant term is the term without 'x'

Answer 25

factored out it becomes Ax + A6 + BX

Answer 26

A6 then?

Answer 27

yes, A6 is same as 6A

Answer 28

equating the constant terms both sides :-

1 = 6A

Answer 29

solve A

Answer 30

1/6

Answer 31

thats right, wat about B ?

Answer 32

x = AX + BX = 1 = A+B

Answer 33

1 = 1/6 + B -> B = 5/6

Answer 34

yes !
so A = 1/6
B = 5/6

Answer 35

Thank you

Answer 36

plug them be
\(\large \frac{x+1}{x(x+6)} = \frac{A}{x} + \frac{B}{x+6} \)

Answer 37

*below

Answer 38

u wlc :)

Answer 39

Ok, got it thanks!