megannicole51
  • megannicole51
Integrate 3x+6/x^2-3x+2 so i just need help with the end of the problem.... i have x(A+B)+A(-1)+B(-2)=3x+6 @pgpilot326
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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megannicole51
  • megannicole51
i got A=9 and B=-9
anonymous
  • anonymous
gotta do it the hard way, huh?
anonymous
  • anonymous
don't you get \[\frac{3x+6}{x^{2}-3x+2}=\frac{A}{x-1}+\frac{B}{x-2}\]

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megannicole51
  • megannicole51
i have to write it out on my homework:/
anonymous
  • anonymous
then do what @satellite73 was showing you ...
megannicole51
  • megannicole51
my -1 and -2 are switched on mine bt yeah
anonymous
  • anonymous
so from yours... A+B=3 and -A-2B=6 just solve the system
anonymous
  • anonymous
\[\frac{3x+6}{(x-2)(x-1)}=\frac{A}{x-2}+\frac{B}{x-1}\] \[A=\frac{3\times 2+6}{2-1}\]
anonymous
  • anonymous
\(B=-9\) is correct, yes
megannicole51
  • megannicole51
9ln(abs(x-2))-9ln(abs(x-1))+c so why isnt my answer right?:(
anonymous
  • anonymous
because \(A=12\) not \(9\)
anonymous
  • anonymous
12 ln(abs(x-2)) -8ln(abs(x-1)) +C
anonymous
  • anonymous
oops... 9 not 8
megannicole51
  • megannicole51
let me check my math
anonymous
  • anonymous
\[A=\frac{3\times 2+6}{2-1}=\frac{12}{1}=12\]
megannicole51
  • megannicole51
got it! thank you!!!
anonymous
  • anonymous
\[\frac{ 3x+6 }{x ^{2}-3x+2 }=\frac{ 3x+6 }{x ^{2}-2x-1x+2 }=\frac{3x+6 }{ x \left( x-2 \right)-1(x-2) }\] \[=\frac{ 3x+6 }{ \left( x-2 \right)\left( x-1 \right) }=\frac{3*2+6 }{\left( x-2 \right)\left( 2-1 \right) }+\frac{ 3*1+6 }{\left( 1-2 \right)(x-1) }\] \[=\frac{ 12 }{ x-2 }-\frac{ 9 }{x-1 }\] now you can integrate.

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