giannimaraj711 giannimaraj711
  • 02-05-2019
  • Mathematics
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Find the partial fraction decomposition of

Find the partial fraction decomposition of class=

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LammettHash
LammettHash LammettHash
  • 02-05-2019

[tex]\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}[/tex]

[tex]1=a(x-1)+bx[/tex]

If [tex]x=0[/tex], then

[tex]1=-a\implies a=-1[/tex]

If [tex]x=1[/tex], then

[tex]1=b[/tex]

So we have

[tex]\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x[/tex]

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