I can't seem to do this with partial fractions

[skyturnred]

Homework Statement

$\frac{x}{(x+4)^{2}}$

Homework Equations

The Attempt at a Solution

I make the integrand equal to the following:

$\frac{A}{(x+4)}$+$\frac{Bx+C}{(x+4)^{2}}$

Then after finding a common denominator I get

x = A(x+4)$^{2}$+(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]

Homework Statement

$\frac{x}{(x+4)^{2}}$

Homework Equations

The Attempt at a Solution

I make the integrand equal to the following:

$\frac{A}{(x+4)}$+$\frac{Bx+C}{(x+4)^{2}}$

Then after finding a common denominator I get

x = A(x+4)$^{2}$+(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:

$\displaystyle\frac{x}{(x+4)^{2}}=\frac{A}{(x+4)}+ \frac{Bx+C}{(x+4)^{2}}$

Multiplying by (x+4)² gives:

$\displaystyle x=A(x+4)+Bx+C$