anonymous
  • anonymous
Write and Solve Partial Fraction Decomposition of a Rational Expression (LOOK IN FOR EQUATION)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ 2x }{ x ^{3}-1 }\]
UnkleRhaukus
  • UnkleRhaukus
how did you get your first step?
UnkleRhaukus
  • UnkleRhaukus
\[x^3-1=(x-1)(x^2+x+1)\]

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UnkleRhaukus
  • UnkleRhaukus
so \[\frac{2x}{x^3-1}=\frac A{x-1}+\frac {Bx+C}{x^2+x+1}\]
UnkleRhaukus
  • UnkleRhaukus
the factor (x^2+x+1) is quadratic , so the denominator must be linear, not just a scalar
UnkleRhaukus
  • UnkleRhaukus
pardon?
UnkleRhaukus
  • UnkleRhaukus
in where?
UnkleRhaukus
  • UnkleRhaukus
im not sure what you are saying
UnkleRhaukus
  • UnkleRhaukus
from the start.
UnkleRhaukus
  • UnkleRhaukus
\[\frac{2x}{x^3-1}=\frac{2x}{(x-1)(x^2+x+1)}=\frac A{x-1}+\frac {Bx+C}{x^2+x+1}\] \[2x=A(x^2+x+1)+(Bx+C)(x-1)\] to find the constants try x=1 , x=0
anonymous
  • anonymous
Is This Correct? b=-2/3 c=2 a=2/3
UnkleRhaukus
  • UnkleRhaukus
\[\color{red}\checkmark\]great work

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