Resolve into partial fractions:
(x+3)(x+1)/
x(x^2+x+1)
Can anyone please help me out?
2 answers
8/x^3
(x+3)(x+1)/[x(x^2+x+1)] =
A/x + (B + C x)/(x^2 + x + 1)
To find A multiply both sides by x and take the limit x --> 0:
A = 3
To find B and C you can just move the A/x term to the other side and simplify:
(B + C x)/(x^2 + x + 1) =
(x+3)(x+1)/[x(x^2+x+1)] - 3/x =
(x^2 + 4x + 3 - 3 x^2 - 3 x - 3)/[x(x^2+x+1)] =
(-2x^2 + x)/[x(x^2+x+1)] =
(1 - 2x)/(x^2+x+1)
A/x + (B + C x)/(x^2 + x + 1)
To find A multiply both sides by x and take the limit x --> 0:
A = 3
To find B and C you can just move the A/x term to the other side and simplify:
(B + C x)/(x^2 + x + 1) =
(x+3)(x+1)/[x(x^2+x+1)] - 3/x =
(x^2 + 4x + 3 - 3 x^2 - 3 x - 3)/[x(x^2+x+1)] =
(-2x^2 + x)/[x(x^2+x+1)] =
(1 - 2x)/(x^2+x+1)