((x+1)/x)^2-2((x-1)/(x+4))-11=0

解答

(\frac{x + 1}{x})^{2} - 2 (\frac{x - 1}{x + 4}) - 11 = 0

x \approx - 0.23719 \dots, x \approx 0.43892 \dots, x \approx - 3.20173 \dots

求解步骤

(\frac{x + 1}{x})^{2} - 2 (\frac{x - 1}{x + 4}) - 11 = 0

乘以最小公倍数

(x + 1)^{2} (x + 4) - 2 x^{2} (x - 1) - 11 x^{2} (x + 4) = 0

解

(x + 1)^{2} (x + 4) - 2 x^{2} (x - 1) - 11 x^{2} (x + 4) = 0 : x \approx - 0.23719 \dots, x \approx 0.43892 \dots, x \approx - 3.20173 \dots

x \approx - 0.23719 \dots, x \approx 0.43892 \dots, x \approx - 3.20173 \dots

验证解

找到无定义的点（奇点）:

x = 0, x = - 4

将不在定义域的点与解相综合:

x \approx - 0.23719 \dots, x \approx 0.43892 \dots, x \approx - 3.20173 \dots

\frac{21}{2 \cdot x} = \frac{331}{3}

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

so l v e f or x, f (x + h) = \frac{( x ^{2} - 1 )}{( x + 1 )}

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

so l v e f or a, \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1