SOLUTION: Hi guys, Struggeling with the following partial fractions: 1/(x+1)(x^2-1) 1/x^3+2x Any Help To Show Me Steps Of How To Complete The Equations Would Be Much Help, Thank you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Hi guys, Struggeling with the following partial fractions: 1/(x+1)(x^2-1) 1/x^3+2x Any Help To Show Me Steps Of How To Complete The Equations Would Be Much Help, Thank you      Log On


   

Question 357964: Hi guys,
Struggeling with the following partial fractions:
1/(x+1)(x^2-1)
1/x^3+2x
Any Help To Show Me Steps Of How To Complete The Equations Would Be Much Help,
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28%28x%2B1%29%28x%5E2-1%29%29=1%2F%28%28x%2B1%29%28x-1%29%28x%2B1%29%29
1%2F%28%28x%2B1%29%28x%5E2-1%29%29=1%2F%28%28x%2B1%29%5E2%28x-1%29%29
1%2F%28%28x%2B1%29%28x%5E2-1%29%29=A%2F%28x%2B1%29%2BB%2F%28x%2B1%29%5E2%2BC%2F%28x-1%29
Multiply by the denominator,
1=A%28x%2B1%29%28x-1%29%2BB%28x-1%29%2BC%28x%2B1%29%5E2
A%28x%5E2-1%29%2BB%28x-1%29%2BC%28x%5E2%2B2x%2B1%29=1
1.Ax%5E2%2BCx%5E2=0
2.Bx%2B2Cx=0
3.-A-B%2BC=1
From eq. 1,
A=-C
From eq. 2,
B=-2C
Then substituting into eq. 3,
C%2B2C%2BC=1
4C=1
highlight%28C=1%2F4%29
Now back substitute and find A and B.
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.
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1%2F%28x%5E3%2B2x%29=1%2F%28x%28x%5E2%2B2%29%29
1%2F%28x%5E3%2B2x%29=A%2Fx%2B%28Bx%29%2F%28x%5E2%2B2%29
Multiply by the denominator,
1=A%28x%5E2%2B2%29%2BBx%5E2
1.Ax%5E2%2BBx%5E2=0
2.2A=1
From eq. 2,
highlight%28A=1%2F2%29
Then from eq. 1,
B=A
highlight%28B=-1%2F2%29
.
.
.
highlight_green%281%2F%28x%5E3%2B2x%29=1%2F%282x%29-%28x%29%2F%282%28x%5E2%2B2%29%29%29