Question

Someone pls help me ASAP! Express the following as the sum of its partial fraction: 2x+4/x(x+2)(x-4)​

Answer 1

Explanation:

`(2x+4)/(x(x+2)(x-4)) =(a)/(x) +(b)/(x+2) +(c)/(x-4) \\2x+4=a(x+2)(x-4) +bx(x-4)+cx(x+2)\\`

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

`(2x+4)/(x(x+2)(x-4)) =(-1)/(2x) +0+(1)/(2(x-4)) \\(2x+4)/(x(x+2)(x-4)) =(-1)/(2x) +(1)/(2(x-4))`