展开 ((e^x+e^{-x})^2)/4

解答

展开

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

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

求解步骤

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

(e^{x} + e^{- x})^{2} = e^{2 x} + 2 + e^{- 2 x}

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

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

消掉

\frac{2}{4} : \frac{1}{2}

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

e x p an d \frac{8 x - 5}{( 4 x - 7 ) ^{2}}

e x p an d (\frac{4}{2 - 5 x})^{3}

e x p an d \frac{7 ( x + h ) ^{2}}{2}

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