Jika (3x² - x + 2)/[x(x² - 3)] ≡ [(A/x) + (B/(x + 1)) + (C/(x - 1))] nilai A + B + C sama dengan .... A. 0 B. 3 C. 6 D. 5 E. 12

<p>Jawaban : &nbsp;B. 3.</p><p>&nbsp;</p><p>Ingat!<br>Jika (ax²+bx+c) /d = (ex²+fx+g)/d<br>Maka a=e, b=f, c=g.</p><p>x²-y² =(x-y) (x+y).<br>(a+b) (c+d) = ac +ad + bc + bd.</p><p>&nbsp;</p><p><strong>Asumsikan (3x² - x + 2)/[x(x² - 1)] ≡ [(A/x) + (B/(x + 1)) + (C/(x - 1))].</strong></p><p>&nbsp;</p><p>Perhatikan.</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [(A/x) + (B/(x + 1)) + (C/(x - 1))]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [A(x + 1)(x - 1)]/[x(x + 1)(x - 1)] + [Bx(x - 1)]/[x(x + 1)(x - 1)] + [Cx(x + 1)]/[x(x + 1)(x - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [A(x² - 1)]/[x(x² - 1)] + [B(x² - x)]/[x(x² - 1)] + [C(x² + x)]/[x(x² - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [Ax² - A]/[x(x² - 1)] + [Bx² - Bx]/[x(x² - 1)] + [Cx² + Cx]/[x(x² - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [(Ax² - A) + (Bx² - Bx) + (Cx² + Cx)]/[x(x² - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [Ax² - A + Bx² - Bx + Cx² + Cx]/[x(x² - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [Ax² + Bx² + Cx² - Bx + Cx - A]/[x(x² - 1)]</p><p>(3x² - x + 2)/[x(x² - 1)] ≡ [(A + B + C)x² - (B - C)x - A]/[x(x² - 1)]</p><p>Diperoleh</p><p>3x² = (A + B + C)x²</p><p>A + B + C = 3 .....(1)</p><p>&nbsp;</p><p>- x = - (B - C)x</p><p>B - C = 1 .....(2)</p><p>&nbsp;</p><p>2 = -A</p><p>A = -2 .....(3)</p><p>&nbsp;</p><p>Substitusi A = -2 ke A + B + C = 3.</p><p>-2 + B + C = 3</p><p>B + C = 3+2</p><p>B + C = 5 .....(4)</p><p>&nbsp;</p><p>Eliminasi C pada persamaan (2) dan (4)<br>B - C = 1<br>B + C = 5<br>_________+<br>2B = 6</p><p>B = 6/2</p><p>B = 3</p><p>&nbsp;</p><p>Substitusi B = 3 ke B - C = 1.<br>3 - C = 1</p><p>-C = 1-3</p><p>-C = -2</p><p>C = -2/-1</p><p>C = 2</p><p>&nbsp;</p><p>Nilai A = -2, B = 3 dan C = 2, sehingga A + B + C = -2 + 3 + 2 = 3.</p><p>&nbsp;</p><p>Jadi, jawaban yang benar adalah B. 3.</p>