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

1 Answer
Bdub
Mar 8, 2016

(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))

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