((x+1)/x)^2+5((x+1)/x)+4=0

解答

(\frac{x + 1}{x})^{2} + 5 (\frac{x + 1}{x}) + 4 = 0

x = - \frac{1}{5}, x = - \frac{1}{2}

十进制

x = - 0.2, x = - 0.5

求解步骤

(\frac{x + 1}{x})^{2} + 5 (\frac{x + 1}{x}) + 4 = 0

乘以最小公倍数

(x + 1)^{2} + 5 x (x + 1) + 4 x^{2} = 0

解

(x + 1)^{2} + 5 x (x + 1) + 4 x^{2} = 0 : x = - \frac{1}{5}, x = - \frac{1}{2}

x = - \frac{1}{5}, x = - \frac{1}{2}

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 = - \frac{1}{5}, x = - \frac{1}{2}

\frac{- 5 + 3}{4 ∣ 1 - x ∣} = \frac{7}{3}

\frac{( x + 1 )}{x} + ∣ x + 1 ∣ = \frac{( ( x + 1 ) ^{2} )}{∣ x ∣}

f^{- 1} (9) = 2, f^{- 1} (- 8)

\frac{x}{( x - 2 )} - \frac{( x - 2 )}{x} = \frac{5}{2}

\frac{- 3}{( x - 2 ) ^{2}} = 0