What is expand-KL+(U(t-(e^{xt}-1)/x)) ?

The solution to expand-KL+(U(t-(e^{xt}-1)/x)) is -LK+Ut-(e^{tx}U)/x+U/x

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expand-KL+(U(t-(e^{xt}-1)/x))

expand

- K L + (U (t - \frac{e ^{x t} - 1}{x}))

- L K + U t - \frac{e ^{t x} U}{x} + \frac{U}{x}

Solution steps

- K L + (U (t - \frac{e ^{x t} - 1}{x}))

Remove parentheses:

(a) = a

= - K L + U (t - \frac{e ^{x t} - 1}{x})

= - L K + U (t - \frac{e ^{t x} - 1}{x})

Expand

U (t - \frac{e ^{x t} - 1}{x}) : U t - \frac{e ^{t x} U - U}{x}

= - K L + U t - \frac{e ^{t x} U - U}{x}

Apply the fraction rule:

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

\frac{e ^{t x} U - U}{x} = - (\frac{e ^{t x} U}{x}) - (- \frac{U}{x})

= - L K + U t - (\frac{e ^{t x} U}{x}) - (- \frac{U}{x})

Remove parentheses:

(a) = a, - (- a) = a

= - K L + U t - \frac{e ^{t x} U}{x} + \frac{U}{x}

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10 (10 - \frac{e ^{30} - 1}{3 e ^{30}})

What is expand-KL+(U(t-(e^{xt}-1)/x)) ?
The solution to expand-KL+(U(t-(e^{xt}-1)/x)) is -LK+Ut-(e^{tx}U)/x+U/x