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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

\frac{10 s + 4}{s ( s + 1 ) ( s ^{2} + 4 s + 5 )}

e^{2} (y + 2 z) d z

(3 x - 1) (2 x e^{3} + 4 x^{2} - 5)

\frac{( 1 + sin ( x ) ) ^{2}}{2}

\frac{5 z ^{2} ( z + 2 )}{3 z - 1}

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