What is expand ((e^x-e^{-x})^2)/4 ?

The solution to expand ((e^x-e^{-x})^2)/4 is (e^{2x})/4-1/2+(e^{-2x})/4

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expand ((e^x-e^{-x})^2)/4

expand

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

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

Solution steps

\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}

Apply the fraction rule:

\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}

Cancel

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

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

\frac{40}{( s ^{2} + 4 s + 5 ) ^{2}}

\frac{1}{4 + x}

π (6 x + 4)^{2} (8 x + 7)

9 (2 ln (3) + \frac{22}{27})

(1 - \frac{3}{y} + x) d y + (y - \frac{3}{x} + 1) d x

What is expand ((e^x-e^{-x})^2)/4 ?
The solution to expand ((e^x-e^{-x})^2)/4 is (e^{2x})/4-1/2+(e^{-2x})/4