resolve (5x + 3)/x(x- 1)(x+3) into partial fractions.
(5x + 3)/[x(x- 1)(x+3)] = A/x + B/(x- 1) + C/(x+3)
Multiply both sides by x(x- 1)(x+3), giving,
(5x + 3) = A(x – 1)(x + 3) + B.x(x + 3) + C,x(x – 1)
Substitute values for x into the above expression, to evaluate the coefficients.
x = 0
3 = A(-1)(3) + 0 + 0
A = -1
x = 1
8 = 0 + B.1.(4) + 0
B = 2
x = -3
-12 = 0 + 0 + C.(-3)(-4)
C = -1
The partial fractions are: -1/x + 2/(x – 1) – 1/(x + 3)