Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

QRAwarrior

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?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    i am lost. where does this line come from \[6x + 22 = Ax + 2A + Bx - 4B\]

    • 2 years ago
  2. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    oh nvm i see the mistake

    • 2 years ago
  3. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    6x + 22/(x+2)(x-4) dx

    • 2 years ago
  4. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the mistake?

    • 2 years ago
  5. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    Let x = -2. Then, 6(2) + 22 = A(-2 + 2) + B(-2 - 4)

    • 2 years ago
  6. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    should be Let x = -2. Then, 6(-2) + 22 = A(-2 + 2) + B(-2 - 4)

    • 2 years ago
  7. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I actually did it with -2, and then this is what I got: 6x + 22 = A(x + 2) + B(x-4). Let x = -2. Then, 6(-2) + 22 = A(-2 + 2) + B(-2-4) -12 + 22 = B(-6) 10/6 = -B -10/6 = B....

    • 2 years ago
  8. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    6x+22=(a+b)x+(2a-4b) now comparing both sides 6=a+b 22=(2a-4b) now solve two equations you will get a and b

    • 2 years ago
  9. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    @SUROJ I did that for "No Trick"

    • 2 years ago
  10. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    \[a+b=6\] \[a+2b=11\] \[b=5\]

    • 2 years ago
  11. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    What am I doing wrong wrt the trick? Why am I not getting the same answer as the second method?

    • 2 years ago
  12. .Sam.
    Best Response
    You've already chosen the best response.
    Medals 0

    (6x+22)/((x+2)(x-4)) Factor out the 2, 2(3x+11)/((x+2)(x-4)) ---------------------------------------- A/(x+2)+B/(x-4) ---------------------------------------- 6=A+B 22=-4A+2B ---------------------------------------- A=-5/3 B=23/3 -(5)/(3(x+2))+(23)/(3(x-4))

    • 2 years ago
  13. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    i see mistake when you put 6(2) in place of 6(-2) ....in first trick

    • 2 years ago
  14. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    did you see that?

    • 2 years ago
  15. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    ok lets start at the top is it \[\frac{6x + 22 }{(x+2)(x-4)}=\frac{a}{x+2}+\frac{b}{x-4}\]

    • 2 years ago
  16. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok folks, the point here is that the "Trick" does not match with "No Trick" for the below solution: 6x + 22 = A(x + 2) + B(x-4). Let x = -2. Then, 6(-2) + 22 = A(-2 + 2) + B(-2-4) -12 + 22 = B(-6) 10/6 = -B -10/6 = B....

    • 2 years ago
  17. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73 Yes

    • 2 years ago
  18. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    Let 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

    • 2 years ago
  19. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    @SUROJ Look at my recent one

    • 2 years ago
  20. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    that's right

    • 2 years ago
  21. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    Then why is it NOT the same as "No trick"?

    • 2 years ago
  22. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so we can do this by writing \[6x+22=A(x+2)+B(x-4)\] \[-12+22=-6B\] \[10=-6B\] \[-\frac{5}{3}\] and likewise \[A=\frac{23}{3}\] so give \[\frac{6x+22}{(x+2)(x-4)}=\frac{23}{3(x+2)}-\frac{5}{3(x+4)}\]

    • 2 years ago
  23. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    a+b=6 is same as 2(a+b)=2(6) is same as 2a+2b=12 is same as -2a -2b =-12 add -2a-2b=-12 and 2a-4b=22

    • 2 years ago
  24. QRAwarrior
    Best Response
    You've already chosen the best response.
    Medals 0

    Alright, then how about the "No trick"?

    • 2 years ago
  25. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    typo on last line should be \[\frac{6x+22}{(x+2)(x-4)}=\frac{23}{3(x+2)}-\frac{5}{3(x-4)}\]

    • 2 years ago
  26. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    add left left and right right -2a-2b=-12 and 2a-4b=22 gives -6b=10 so b is -10/6 same as first one

    • 2 years ago
  27. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    now we try with "no trick" \[6x+22=A(x-4)+B(x+2)\] \[6x+22=Ax-4A+Bx+2B\] \[6x+22=(A+B)x+2B-4A\] \[A+B=6\] \[2B-4A=22\]

    • 2 years ago
  28. satellite73
    Best Response
    You've already chosen the best response.
    Medals 0

    i get the same answer solving this one

    • 2 years ago
  29. SUROJ
    Best Response
    You've already chosen the best response.
    Medals 2

    yes.....

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.