1/((x^2+1))+1/((x-1))= 6/5

解

\frac{1}{( x ^{2} + 1 )} + \frac{1}{( x - 1 )} = \frac{6}{5}

x = 2, x = - \frac{1}{12} + i \frac{71}{12}, x = - \frac{1}{12} - i \frac{71}{12}

解答ステップ

\frac{1}{( x ^{2} + 1 )} + \frac{1}{( x - 1 )} = \frac{6}{5}

LCMで乗じる

5 (x - 1) + 5 (x^{2} + 1) = 6 (x - 1) (x^{2} + 1)

解く

5 (x - 1) + 5 (x^{2} + 1) = 6 (x - 1) (x^{2} + 1) : x = 2, x = - \frac{1}{12} + i \frac{71}{12}, x = - \frac{1}{12} - i \frac{71}{12}

x = 2, x = - \frac{1}{12} + i \frac{71}{12}, x = - \frac{1}{12} - i \frac{71}{12}

解を検算する

未定義の (特異) 点を求める:

x = 1

未定義のポイントを解に組み合わせる:

x = 2, x = - \frac{1}{12} + i \frac{71}{12}, x = - \frac{1}{12} - i \frac{71}{12}