Question

How do you express `(x+1)/(x^2 + 6x)` in partial fractions?

Answer 1

`(x+1)/(x(x+6)) = (1/6)/x + (5/6)/(x+6) = 1/(6x)+5/(6(x+6))`

Explanation:

`(x+1)/(x(x+6)) = A/x + B/(x+6)`
`(x+1)=A(x+6)+Bx`
`x+1 = Ax+6A+Bx`
`1=A+B, 6A=1`
`A=1/6 , B=1-1/6 =5/6`
`(x+1)/(x(x+6)) = (1/6)/x + (5/6)/(x+6) = 1/(6x)+5/(6(x+6))`