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HelpMe94

  • 3 years ago

Write and Solve Partial Fraction Decomposition of a Rational Expression (LOOK IN FOR EQUATION)

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  1. HelpMe94
    • 3 years ago
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    \[\frac{ 2x }{ x ^{3}-1 }\]

  2. UnkleRhaukus
    • 3 years ago
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    how did you get your first step?

  3. UnkleRhaukus
    • 3 years ago
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    \[x^3-1=(x-1)(x^2+x+1)\]

  4. UnkleRhaukus
    • 3 years ago
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    so \[\frac{2x}{x^3-1}=\frac A{x-1}+\frac {Bx+C}{x^2+x+1}\]

  5. UnkleRhaukus
    • 3 years ago
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    the factor (x^2+x+1) is quadratic , so the denominator must be linear, not just a scalar

  6. UnkleRhaukus
    • 3 years ago
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    pardon?

  7. UnkleRhaukus
    • 3 years ago
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    in where?

  8. UnkleRhaukus
    • 3 years ago
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    im not sure what you are saying

  9. UnkleRhaukus
    • 3 years ago
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    from the start.

  10. UnkleRhaukus
    • 3 years ago
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    \[\frac{2x}{x^3-1}=\frac{2x}{(x-1)(x^2+x+1)}=\frac A{x-1}+\frac {Bx+C}{x^2+x+1}\] \[2x=A(x^2+x+1)+(Bx+C)(x-1)\] to find the constants try x=1 , x=0

  11. HelpMe94
    • 3 years ago
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    Is This Correct? b=-2/3 c=2 a=2/3

  12. UnkleRhaukus
    • 3 years ago
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    \[\color{red}\checkmark\]great work

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