What is expand (e^t*(cos(t)-1))/t ?

The solution to expand (e^t*(cos(t)-1))/t is (e^tcos(t))/t-(e^t)/t

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expand (e^t*(cos(t)-1))/t

expand

\frac{e ^{t} \cdot ( cos ( t ) - 1 )}{t}

\frac{e ^{t} cos ( t )}{t} - \frac{e ^{t}}{t}

Solution steps

\frac{e ^{t} ( cos ( t ) - 1 )}{t}

Expand

e^{t} (cos (t) - 1) : e^{t} cos (t) - e^{t}

= \frac{e ^{t} cos ( t ) - e ^{t}}{t}

Apply the fraction rule:

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

\frac{e ^{t} cos ( t ) - e ^{t}}{t} = \frac{e ^{t} cos ( t )}{t} - \frac{e ^{t}}{t}

= \frac{e ^{t} cos ( t )}{t} - \frac{e ^{t}}{t}

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

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

e^{x} (x + 2 y)

(x - 2) e^{x} + 1

π (e - 1)

What is expand (e^t*(cos(t)-1))/t ?
The solution to expand (e^t*(cos(t)-1))/t is (e^tcos(t))/t-(e^t)/t