Question

当a为何值时,关于x的方程x∕x+3＝2＋a∕x＋3会产生增根？

Answer 1

解：x/(x + 3) =2 + a/(x + 3) => (x – a)/(x + 3) – 2(x + 3)/(x + 3) = 0 => (x – a – 2x –6)/(x + 3) = 0 => (-x – a – 6)/(x + 3) = 0 => (x + a + 6)/(x + 3) = 0=> x + a + 6 = 0而且x + 3 ≠ 0 => x = -a – 6而且x ≠ -3，如果原方程有增根，说明-a – 6 = -3=> a = -3，所以当 a = -3 时，原方程有增根。

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