4/(2+e^x)= 6/(3+e^{-x)}

解答

\frac{4}{2 + e ^{x}} = \frac{6}{3 + e ^{- x}}

x = \frac{1}{2} ln (\frac{2}{3})

十进制

x = - 0.20273 \dots

求解步骤

\frac{4}{2 + e ^{x}} = \frac{6}{3 + e ^{- x}}

整理后得

\frac{4}{2 + e ^{x}} = \frac{6 e ^{x}}{3 e ^{x} + 1}

使用分式交叉相乘

4 (3 e^{x} + 1) = (2 + e^{x}) \cdot 6 e^{x}

解

4 (3 e^{x} + 1) = (2 + e^{x}) \cdot 6 e^{x} : x = \frac{1}{2} ln (\frac{2}{3})

x = \frac{1}{2} ln (\frac{2}{3})

\frac{5 v - 5}{v} - \frac{5 v + 15}{v} = 1

\frac{24}{x} = 3

\frac{5}{x ^{2}} - \frac{38}{x} = 16

1 + \frac{7}{x - 2} = \frac{3 x + 7}{x ^{2} - 4}

\frac{2 x - 3}{2} + \frac{5 x}{x + 1} = x