We're looking for [tex]a,b[/tex] such that
[tex]\dfrac{9x-20}{(x+6)^2}=\dfrac a{x+6}+\dfrac b{(x+6)^2}[/tex]
Multiplying both sides by [tex](x+6)^2[/tex] gives us
[tex]9x-20=a(x+6)+b[/tex]
Notice that when [tex]x=-6[/tex], the term involving [tex]a[/tex] vanishes and we're left with
[tex]9(-6)-20=b\implies b=-74[/tex]
Then
[tex]9x-20=a(x+6)-74=ax+6a-74\implies a=9[/tex]
so that
[tex]\dfrac{9x-20}{(x+6)^2}=\boxed{\dfrac9{x+6}-\dfrac{74}{(x+6)^2}}[/tex]
