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

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

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expand ((e^x-e^{-x})^2)/4+1

expand

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

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

Solution steps

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

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

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

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} + 1

Cancel

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

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

A (8, 2) B (3, - 4)

\frac{( x + 2 ) ( x - 1 )}{( x + 3 ) ^{2} ( x - 4 )}

b cs in (b + c) (cot (b) + cot (c))

f (t) (t, sin (3 t) - 1, cos (3 t))

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