Solution:

Given 4x+44/(x²+12+32)=4x+44/[(x+8)(x+4)]

4x+44/[(x+8)(x+4)]=A/(x+8)+B/(x+4)

4x+44=A(x+4)+B(x+8).........(1)

put x=-4 in (1)

we get B=7

put x=-8 in (1)

we get A=-3

there for the 4x+44/(x²+12+32)=-3/(x+8)+7(x+4)

Solution:

Given 2x+5/(x²-6x+9)=2x+5/(x-3)²

2x+5/(x-3)²=A/(x-3)+B/(x-3)²

2x+5=A(x-3)²+B(x-3)

2x+5=A(x²+9-6x)+B(x-3)

2x+5=Ax²+(-6A+b)x-9A-3B...(1)

solving (1) we get A=0

B=2