text: # Regarding partial fractions
  
  #### PrudensOptimus
  
  hi, the problem is:
  
  &int; (8x-17)/x^2+x-12 dx = &int; .../(x+4)(x-3) dx
  
  so 8x - 17 = A(x-3) + B(x+4)
  
  (A+B)x + 4B - 3A
  
  so we have 2 eq and 2 unknown
  
  A+B = 8
  4B-3A = -17
  
  ... but the book says it's suppose to be 4A - 3B,.. I don't know what I did wrong.
  
  Please help.
  
  #### jamesrc
  
  Science Advisor
  Gold Member
  They probably just defined A and B differently than you did. (They must have said (8x-17)/(x2+x-12) = A/(x-3) + B/(x+4) ). You'll still get the right answer your way.
  
  #### PrudensOptimus
  
  the ending result is different...
  
  they got B = 7 and A = 1...
  
  I got B = 41/7, and A = 15/7
  
  #### Hurkyl
  
  Staff Emeritus
  Science Advisor
  Gold Member
  Well, the B and A you listed aren't solutions to the equations you got...
  
  #### Tom Mattson
  
  Staff Emeritus
  Science Advisor
  Gold Member
  Originally posted by PrudensOptimus
  (A+B)x + 4B - 3A
  
  so we have 2 eq and 2 unknown
  
  A+B = 8
  4B-3A = -17
  You don't have to solve these like that.
  
  so 8x - 17 = A(x-3) + B(x+4)
  Starting from here, just plug in x=+3 and x=-4.
  
  x=3:
  8(3)-17=A(3-3)=B(3+4)
  7=7B
  B=1
  
  x=-4:
  8(-4)-17=A(-4-3)+B(-4+4)
  -49=-7A
  A=7
  
  amazing.
  
  ### Physics Forums Values
  
  We Value Quality
  • Topics based on mainstream science
  • Proper English grammar and spelling
  We Value Civility
  • Positive and compassionate attitudes
  • Patience while debating
  We Value Productivity
  • Disciplined to remain on-topic
  • Recognition of own weaknesses
  • Solo and co-op problem solving
metadata: {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}