1/(((x-1)(x-2)))+1/(((x-2)(x-3)))= 2/3

解

\frac{1}{( ( x - 1 ) ( x - 2 ) )} + \frac{1}{( ( x - 2 ) ( x - 3 ) )} = \frac{2}{3}

x = 0, x = 4

解答ステップ

\frac{1}{( ( x - 1 ) ( x - 2 ) )} + \frac{1}{( ( x - 2 ) ( x - 3 ) )} = \frac{2}{3}

LCMで乗じる

3 (x - 3) + 3 (x - 1) = 2 (x - 1) (x - 2) (x - 3)

解く

3 (x - 3) + 3 (x - 1) = 2 (x - 1) (x - 2) (x - 3) : x = 0, x = 2, x = 4

x = 0, x = 2, x = 4

解を検算する

未定義の (特異) 点を求める:

x = 1, x = 2, x = 3

equationは以下で未定義のため:

2

x = 0, x = 4