fraction decomposition
(4x+44)/(x^2+12x+32)
annnd
(2x+5)/(x^2-6x+9)
thanks a ton!
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