Soal UM Undip 2015, tolong bantuannya

P/x + Q/(x + 1) + R/(x - 1)
= [P(x + 1)(x - 1) + Qx(x - 1) + Rx(x + 1)] / x(x + 1)(x - 1)
= [P(x^2 - 1) + Q(x^2 - x) + R(x^2 + x)] / x(x^2 - 1)
= [Px^2 - P + Qx^2 - Qx + Rx^2 + Rx) / (x^3 - x)
= [(P + Q + R)x^2 + (R - Q)x - P] / (x^3 - x)
= (5x + 3) / (x^3 - x)
1) Konstanta
-P = 3 => P = -3

2) koefisien x
R - Q = 5
R = 5 + Q

3) koefisien x^2
P + Q + R = 0
-3 + Q + (5 + Q) = 0
2Q = -2
Q = -1

R = 5 + Q
R = 5 + (-1)
R = 4

[tex]\displaystyle \frac{5x+3}{x^3-x}=\frac{p}{x}+\frac{q}{x+1}+\frac{r}{x-1}\\\frac{5x+3}{x^3-x}=\frac{p(x^2-1)+q(x^2-x)+r(x^2+x)}{x^3-x}\\\frac{5x+3}{x^3-x}=\frac{px^2-p+qx^2-qx+rx^2+rx}{x^3-x}\\\frac{5x+3}{x^3-x}=\frac{(p+q+r)x^2-(q-r)x-p}{x^3-x}\\\\\therefore\\-p=3\\\boxed{\boxed{p=-3}}\\\\p+q+r=0\\-3+q+r=0\\q+r=3\\\\-(q-r)=5\\q-r=-5\\\\q-r=-5\\\underline{q+r=3}+\\2q~~~~=-2\\\boxed{\boxed{q~~~~~=-1}}\\\\q+r=3\\-1+r=3\\\boxed{\boxed{r=4}}[/tex]