Nyatakan fungsi pecahan berikut menjadi fungsi pecahan sebagian. (7x² + 25x + 6)/[(x² - 2x - 1)(3x - 2)]

<p>Jawaban : [(((351/3 x+65)/(17(x² - 2x - 1))) + (-232/(17(3x - 2)))].</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>(7x² + 25x + 6)/[(x² - 2x - 1)(3x - 2)] ≡ [((Ax+B)/(x² - 2x - 1)) + (C/(3x - 2))]</p><p>(7x² + 25x + 6)/[(x² - 2x - 1)(3x - 2)] ≡ [((Ax+B)(3x - 2)/(x² - 2x - 1)(3x - 2)) + (C(x² - 2x - 1)/(x² - 2x - 1)(3x - 2))]</p><p>7x² + 25x + 6 ≡ (Ax+B)(3x - 2)+C(x² - 2x - 1)</p><p>Untuk x = 2/3 maka</p><p>7.(2/3)² + 25.(2/3) + 6 ≡ (A.(2/3)+B)(3.(2/3) - 2)+C((2/3)² - 2.(2/3) - 1)</p><p>7.(4/9) + (50/3) + 6 ≡ (A(2/3)+B)(2 - 2)+C((4/9) - (4/3) - 1)</p><p>(28/9) + (150/9) + (54/9) ≡ ((2/3)A+B).0+C((4/9) - (12/9) - (9/9))</p><p>(232/9) ≡ C(-17/9)</p><p>C = (232/9).(-9/17)</p><p>C = -232/17</p><p>&nbsp;</p><p>7x² + 25x + 6 ≡ 3Ax²-2Ax+3Bx-2B+Cx² - 2Cx - C</p><p>7x² + 25x + 6 ≡ 3Ax²+Cx²-2Ax+3Bx - 2Cx-2B - C</p><p>7x² + 25x + 6 ≡ (3A+C)x²+(-2A+3B-2C)x-2B - C</p><p>Diperoleh</p><p>3A+C = 7 .....(1)</p><p>-2A+3B-2C = 25 .....(2)</p><p>-2B - C = 6 .....(3)</p><p>&nbsp;</p><p>Kurangkan persamaan 1 dan 3.</p><p>3A+C = 7<br>-2B - C = 6<br>_________-</p><p>3A+2B+2C = 1 .....(4)</p><p>&nbsp;</p><p>Eliminasi C pada persamaan (2) dan (4).<br>-2A+3B-2C = 25<br>3A+2B+2C = 1<br>_____________+<br>A+5B = 26</p><p>&nbsp;</p><p>Substitusi C = -232/17 ke 3A+C = 7.</p><p>3A+(-232/17) = 7</p><p>3A = 7 + (232/17)</p><p>3A = 119/17 + 232/17</p><p>3A = 351/17</p><p>A = 351/17 . 1/3</p><p>A = 351/51</p><p><br>Substitusi C = -232/17 ke -2B - C = 6.</p><p>-2B - (-232/17) = 6</p><p>-2B + 232/17 = 6</p><p>2B = 232/17 - 6</p><p>2B = 232/17 - 102/17</p><p>2B = 130/17</p><p>B = 130/17 . 1/2</p><p>B = 65/17</p><p>&nbsp;</p><p>Nilai A = 351/51, B = 65/17 dan C = -232/17, sehingga&nbsp;</p><p>(7x² + 25x + 6)/[(x² - 2x - 1)(3x - 2)]&nbsp;</p><p>≡ [(((351/51 x+65/17)/(x² - 2x - 1)) + ((-232/17)/(3x - 2))]</p><p>≡ [(((351/3 x+65)/(17(x² - 2x - 1))) + (-232/(17(3x - 2)))]</p><p>&nbsp;</p><p>Jadi, jawaban yang benar adalah [(((351/3 x+65)/(17(x² - 2x - 1))) + (-232/(17(3x - 2)))].</p>