Answer:
Step-by-step explanation:
[tex]\frac{2x+4}{x(x+2)(x-4)} =\frac{a}{x} +\frac{b}{x+2} +\frac{c}{x-4} \\2x+4=a(x+2)(x-4) +bx(x-4)+cx(x+2)\\[/tex]
put x=0
0+4=a(0+2)(0-4)+0+0
-8a=4
a=-4/8=-1/2
put x+2=0 or x=-2
2(-2)+4=0+b(-2)(-2-4)+0
12b=0
b=0
put x-4=0 or x=4
2(4)+4=0+0+c(4)(4+2)
24c=12
c=12/24=1/2
[tex]\frac{2x+4}{x(x+2)(x-4)} =\frac{-1}{2x} +0+\frac{1}{2(x-4)} \\\frac{2x+4}{x(x+2)(x-4)} =\frac{-1}{2x} +\frac{1}{2(x-4)}[/tex]
