Question

9x-20/(x+6)^2 partial fraction decomposition

Answer 1

Find the partial fraction decomposition of 6x+8/x2-9x+8

Explanation:

Answer 2

We're looking for
`a,b` such that

`(9x-20)/((x+6)^2)=\frac a{x+6}+\frac b{(x+6)^2}`

Multiplying both sides by
`(x+6)^2` gives us

`9x-20=a(x+6)+b`

Notice that when
`x=-6`, the term involving
`a` vanishes and we're left with

`9(-6)-20=b\implies b=-74`

Then

`9x-20=a(x+6)-74=ax+6a-74\implies a=9`

so that

`(9x-20)/((x+6)^2)=\boxed{\frac9{x+6}-(74)/((x+6)^2)}`