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