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QRAwarrior
 3 years ago
6x + 22 = A(x + 2) + B(x  4)
^I am doing partial fraction decomposition and this is what I am at.
Attempt:
"Trick"
Let x = 2. Then,
6(2) + 22 = A(2 + 2) + B(2  4)
12 + 22 = 0 + B(6)
34 = 6B
34/6 = B

"No Trick"
6x + 22 = Ax + 2A + Bx  4B
(LHS = RHS, then coeff's are equal),
6 = A + B, [1]
22 = 2A  4B
=> 11 = A  2B, [2a]
[2a]  [1],
5 = 0 B
=> 5 = B.
Why aren't the two answers the same?
QRAwarrior
 3 years ago
6x + 22 = A(x + 2) + B(x  4) ^I am doing partial fraction decomposition and this is what I am at. Attempt: "Trick" Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(2  4) 12 + 22 = 0 + B(6) 34 = 6B 34/6 = B  "No Trick" 6x + 22 = Ax + 2A + Bx  4B (LHS = RHS, then coeff's are equal), 6 = A + B, [1] 22 = 2A  4B => 11 = A  2B, [2a] [2a]  [1], 5 = 0 B => 5 = B. Why aren't the two answers the same?

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i am lost. where does this line come from \[6x + 22 = Ax + 2A + Bx  4B\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0oh nvm i see the mistake

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.06x + 22/(x+2)(x4) dx

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0What is the mistake?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(2  4)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0should be Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(2  4)

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0Ok I actually did it with 2, and then this is what I got: 6x + 22 = A(x + 2) + B(x4). Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(24) 12 + 22 = B(6) 10/6 = B 10/6 = B....

SUROJ
 3 years ago
Best ResponseYou've already chosen the best response.26x+22=(a+b)x+(2a4b) now comparing both sides 6=a+b 22=(2a4b) now solve two equations you will get a and b

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0@SUROJ I did that for "No Trick"

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[a+b=6\] \[a+2b=11\] \[b=5\]

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0What am I doing wrong wrt the trick? Why am I not getting the same answer as the second method?

.Sam.
 3 years ago
Best ResponseYou've already chosen the best response.0(6x+22)/((x+2)(x4)) Factor out the 2, 2(3x+11)/((x+2)(x4))  A/(x+2)+B/(x4)  6=A+B 22=4A+2B  A=5/3 B=23/3 (5)/(3(x+2))+(23)/(3(x4))

SUROJ
 3 years ago
Best ResponseYou've already chosen the best response.2i see mistake when you put 6(2) in place of 6(2) ....in first trick

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok lets start at the top is it \[\frac{6x + 22 }{(x+2)(x4)}=\frac{a}{x+2}+\frac{b}{x4}\]

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0Ok folks, the point here is that the "Trick" does not match with "No Trick" for the below solution: 6x + 22 = A(x + 2) + B(x4). Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(24) 12 + 22 = B(6) 10/6 = B 10/6 = B....

SUROJ
 3 years ago
Best ResponseYou've already chosen the best response.2Let x = 2. Then, 6(2) + 22 = A(2 + 2) + B(2  4)  in this step 12 + 22 = 0 + B(6) 34 = 6B 34/6 = B

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0@SUROJ Look at my recent one

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0Then why is it NOT the same as "No trick"?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok so we can do this by writing \[6x+22=A(x+2)+B(x4)\] \[12+22=6B\] \[10=6B\] \[\frac{5}{3}\] and likewise \[A=\frac{23}{3}\] so give \[\frac{6x+22}{(x+2)(x4)}=\frac{23}{3(x+2)}\frac{5}{3(x+4)}\]

SUROJ
 3 years ago
Best ResponseYou've already chosen the best response.2a+b=6 is same as 2(a+b)=2(6) is same as 2a+2b=12 is same as 2a 2b =12 add 2a2b=12 and 2a4b=22

QRAwarrior
 3 years ago
Best ResponseYou've already chosen the best response.0Alright, then how about the "No trick"?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0typo on last line should be \[\frac{6x+22}{(x+2)(x4)}=\frac{23}{3(x+2)}\frac{5}{3(x4)}\]

SUROJ
 3 years ago
Best ResponseYou've already chosen the best response.2add left left and right right 2a2b=12 and 2a4b=22 gives 6b=10 so b is 10/6 same as first one

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0now we try with "no trick" \[6x+22=A(x4)+B(x+2)\] \[6x+22=Ax4A+Bx+2B\] \[6x+22=(A+B)x+2B4A\] \[A+B=6\] \[2B4A=22\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i get the same answer solving this one
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