tolong caranya ya...

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) + Qx^2 - Qx + Rx^2 + Rx) / 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)

Konstanta
-P = 3 => P = -3

Koefisien x
R - Q = 5 => R = Q + 5

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

R = Q + 5 => R = -1 + 5 => 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+1)(x-1) + Q(x)(x-1) + R(x)(x+1)}{x(x+1)(x-1)} \\ \frac{5x+3}{x^{3}-x} = \frac{Px^2-P+Qx^2-Qx+Rx^2+Rx}{x^3-x} \\ P+Q+R = 0 \\ -Q+R = 5 \\ -P = 3 -\ \textgreater \ P = -3 -3+Q+R = 0 \\ -Q+R = 5 \\ Q = -1 \\ R = 4 \\ P = -3; Q = -1; R = 4 (E) -\ \textgreater \ Jawab [/tex]