1/x+1/x-4= 2/(x^2)-4x

解答

\frac{1}{x} + \frac{1}{x} - 4 = \frac{2}{x ^{2}} - 4 x

x = 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

求解步骤

\frac{1}{x} + \frac{1}{x} - 4 = \frac{2}{x ^{2}} - 4 x

乘以最小公倍数

2 x - 4 x^{2} = 2 - 4 x^{3}

解

2 x - 4 x^{2} = 2 - 4 x^{3} : x = 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

x = 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

验证解

找到无定义的点（奇点）:

x = 0

将不在定义域的点与解相综合:

x = 1, x = \frac{1}{2} i, x = - \frac{1}{2} i

\frac{x - 4}{x - 2} = \frac{- 3}{4}

\frac{( 1 ) x + 1}{x} = \frac{21}{20}

\frac{x - 3}{x} = x^{2}

\frac{12}{30} = \frac{( 2 x )}{( 4 x + 10 )}

\frac{y ^{2}}{4 - 5 y + 16} = 0