What is expand (e^{-6x}(e^{6x}-1)^2)/4+1 ?

The solution to expand (e^{-6x}(e^{6x}-1)^2)/4+1 is (e^{6x})/4-1/2+(e^{-6x})/4+1

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expand (e^{-6x}(e^{6x}-1)^2)/4+1

expand

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} + 1

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

Solution steps

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} + 1

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} = \frac{e ^{6 x} - 2 + e ^{- 6 x}}{4}

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

Apply the fraction rule:

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

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

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

Cancel

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

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

\frac{10 ( 10 + 730 )}{7}

\frac{( - 12 x ^{2} - 192 x + 2304 )}{( x + 8 ) ^{2}}

\frac{X}{X ^{2}}

- 2^{10}

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

What is expand (e^{-6x}(e^{6x}-1)^2)/4+1 ?
The solution to expand (e^{-6x}(e^{6x}-1)^2)/4+1 is (e^{6x})/4-1/2+(e^{-6x})/4+1