Jika (5x + 3)/[(x + 3)(1 - 2x)] ≡ [(A/(x + 3)) + (B/(1 - 2x))] nilai A + B adalah .... A. -(1/7) B. (2/7) C. (3/7) D. (4/7) E. (5/7)

<p>Jawaban : &nbsp;A. -(1/7).</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>(a+b) (c+d) = ac +ad + bc + bd.</p><p>&nbsp;</p><p>Perhatikan.</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [(A/(x + 3)) + (B/(1 - 2x))]</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [A(1 - 2x)]/[(x + 3)(1 - 2x)] + [B(x + 3)]/[(x + 3)(1 - 2x)]</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [A - 2Ax]/[(x + 3)(1 - 2x)] + [Bx + 3B]/[(x + 3)(1 - 2x)]</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [A - 2Ax &nbsp;+ Bx + 3B]/[(x + 3)(1 - 2x)]</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [- 2Ax &nbsp;+ Bx + A + 3B]/[(x + 3)(1 - 2x)]</p><p>(5x + 3)/[(x + 3)(1 - 2x)] ≡ [(-2A &nbsp;+ B)x + (A + 3B)]/[(x + 3)(1 - 2x)]</p><p>&nbsp;</p><p>Diperoleh</p><p>5x = (-2A &nbsp;+ B)x</p><p>5 = -2A &nbsp;+ B</p><p>-2A &nbsp;+ B = 5 .....(1)</p><p>&nbsp;</p><p>3 = A + 3B</p><p>A + 3B = 3 .....(2)</p><p>&nbsp;</p><p>Eliminasi A pada persamaan (1) dan (2)<br>-2A &nbsp;+ B = 5<br>A + 3B = 3 &nbsp;(kedua ruas dikali 2)</p><p>&nbsp;</p><p>-2A &nbsp;+ B = 5<br>2A + 6B = 6<br>_________+<br>7B = 11</p><p>B = 11/7</p><p>&nbsp;</p><p>Substitusi B = 11/7 ke -2A &nbsp;+ B = 5.<br>-2A &nbsp;+ 11/7 = 5</p><p>-2A &nbsp;= 5 - 11/7</p><p>-2A &nbsp;= 35/7 - 11/7</p><p>-2A &nbsp;= 24/7</p><p>A &nbsp;= 24/7 x (-1/2)</p><p>A &nbsp;= -12/7</p><p>&nbsp;</p><p>Nilai A &nbsp;= -12/7 dan B = 11/7, sehingga&nbsp;</p><p>A + B = -12/7 + 11/7</p><p>A + B = -1/7</p><p>&nbsp;</p><p>Jadi, jawaban yang benar adalah A. -(1/7).</p>