CPM Homework Help : PC3 Problem 4-63

What are the values of $A$ and $B$ in the equation $\frac { 1 } { x ^ { 2 } + 5 x + 4 } = \frac { A } { x + 4 } + \frac { B } { x + 1 }$ ?

Step 1:

$\frac{A(x+1)}{(x+4)(x+1)}+\frac{B(x+4)}{(x+1)(x+4)}$

Step 2:

$A(x+1) + B(x+4)=1$
Why?

Step 3:

$Ax+A+Bx+4B=1$

Step 4:

Solve:
$Ax+Bx=0x$
$A+4B=1$