Factor
\frac{tu\left(e^{t}-1\right)}{e^{3t}}
Evaluate
\frac{tu\left(e^{t}-1\right)}{e^{3t}}
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ut\left(\frac{1}{e^{2t}}-\frac{1}{e^{3t}}\right)
Factor out ut.
\frac{1-\frac{1}{e^{t}}}{\left(e^{t}\right)^{2}}
Consider \left(e^{t}\right)^{-2}-\left(e^{t}\right)^{-3}. Factor out \frac{1}{\left(e^{t}\right)^{2}}.
\frac{ut\left(1-\frac{1}{e^{t}}\right)}{\left(e^{t}\right)^{2}}
Rewrite the complete factored expression.
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