megannicole51
  • megannicole51
Split into partial fractions.... 5(1+s)/s(s^2+6s+5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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megannicole51
  • megannicole51
so i know the denominator factors into s(s+3)(s+2)
anonymous
  • anonymous
good what is next ?
megannicole51
  • megannicole51
i have to split it up in 3 different fractions?

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megannicole51
  • megannicole51
A, B, and C?
anonymous
  • anonymous
yes
megannicole51
  • megannicole51
so ill have A/s + B/(s+3) + C/(s+2) ?
anonymous
  • anonymous
yes!
megannicole51
  • megannicole51
yay!
megannicole51
  • megannicole51
so this is where i get mixed up so hold on lol
megannicole51
  • megannicole51
so then i set A+B+C=5(1+s)?
megannicole51
  • megannicole51
or cross multiply first?
anonymous
  • anonymous
now you should multiply both sides by s(s+3)(s+2)
dan815
  • dan815
we gotta get common denominator right
dan815
  • dan815
how can A+b +c equal that otherwise
megannicole51
  • megannicole51
so like A (s(s+3)(s+2))?
anonymous
  • anonymous
A(s(s+3)(s+2))/s + B(s(s+3)(s+2))/(s+3) + C(s(s+3)(s+2))/(s+2) = 5(1+s)
dan815
  • dan815
|dw:1378417489108:dw|
anonymous
  • anonymous
this is how it looks when you multiply both sides by the denominator
megannicole51
  • megannicole51
okay yes thats what ive got!
dan815
  • dan815
fix your factoring first
megannicole51
  • megannicole51
dan ur confusing me
anonymous
  • anonymous
@dan815 is right by the way s(s^2+6s+5) = s(s+5)(s+1)
dan815
  • dan815
|dw:1378417612993:dw|
dan815
  • dan815
|dw:1378417677455:dw|
dan815
  • dan815
|dw:1378417730533:dw|
megannicole51
  • megannicole51
so A/s + B/(s+5) ?
anonymous
  • anonymous
yes
megannicole51
  • megannicole51
thanks Dan that was my fault i was looking at the wrong problem when i factored the denominator!
megannicole51
  • megannicole51
so now cross multiply?
dan815
  • dan815
yw
anonymous
  • anonymous
yes now multiply both sides by s(s+5) (the denominator)
megannicole51
  • megannicole51
A(s+5)+B(s)/s(s+5)
dan815
  • dan815
cross multiply what?
megannicole51
  • megannicole51
the split fractions
dan815
  • dan815
you must get common denominator now so you can solve for a and b
dan815
  • dan815
|dw:1378418207760:dw|
anonymous
  • anonymous
5/[s(s+5)] = A/s + B/(s+5)
anonymous
  • anonymous
multiply both sides by s(s+5) ..
dan815
  • dan815
you get common denominator so you can equate the numerators and solve for a and b
dan815
  • dan815
we can extract 2 system of equations in this case from the numerator conditions one for the coefficient of s and the constant
dan815
  • dan815
|dw:1378418299974:dw|
dan815
  • dan815
after you solve for a and b you can write your a/s + b/s+5 function
dan815
  • dan815
this is pretty much how all your examplse will go
dan815
  • dan815
im sure your next question will involve some quadratic for the partial fractions we do the same thing, you split the numerators into some number of equations and solve some number of unknowns

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