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I can't seem to do this with partial fractions

  • Thread starter skyturnred
  • Start date
1. The problem statement, all variables and given/known data

[itex]\frac{x}{(x+4)^{2}}[/itex]

2. Relevant equations



3. The attempt at a solution

I make the integrand equal to the following:

[itex]\frac{A}{(x+4)}[/itex]+[itex]\frac{Bx+C}{(x+4)^{2}}[/itex]

Then after finding a common denominator I get

x = A(x+4)[itex]^{2}[/itex]+(Bx+C)(x+4)

But that cannot be possible because when you set x=-4, you get -4=0. Any help please?

Also if you have ANY tips whatsoever about partial fractions please tell me them!
 

SammyS

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1. The problem statement, all variables and given/known data

[itex]\frac{x}{(x+4)^{2}}[/itex]

2. Relevant equations



3. The attempt at a solution

I make the integrand equal to the following:

[itex]\frac{A}{(x+4)}[/itex]+[itex]\frac{Bx+C}{(x+4)^{2}}[/itex]

Then after finding a common denominator I get

x = A(x+4)[itex]^{2}[/itex]+(Bx+C)(x+4)

But that cannot be possible because when you set x=-4, you get -4=0. Any help please?

Also if you have ANY tips whatsoever about partial fractions please tell me them!
Algebra check:

[itex]\displaystyle\frac{x}{(x+4)^{2}}=\frac{A}{(x+4)}+ \frac{Bx+C}{(x+4)^{2}}[/itex]

Multiplying by (x+4)2 gives:

[itex]\displaystyle x=A(x+4)+Bx+C[/itex]
 

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