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

解答

\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}

求解步骤

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

乘以最小公倍数

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

解

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}

验证解

找到无定义的点（奇点）:

x = 1

将不在定义域的点与解相综合:

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

so l v e f or x, \frac{3}{x} + \frac{2}{y} = 0

\frac{3 x}{7 x + 20} = \frac{24}{76}

- x - 2 - 7 x (\frac{1}{x} - \frac{1}{2}) = \frac{( 1 + \frac{x}{2} )}{2} + \frac{11}{2}

\frac{20}{5} = \frac{30}{x}

\frac{( x - 2 )}{x} + \frac{4}{( x - 2 )} = \frac{8}{( x ^{2} - 2 x )}