Factor
\frac{\left(t+2\right)e^{\frac{t}{2}}}{2}
Evaluate
\frac{\left(t+2\right)e^{\frac{t}{2}}}{2}
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\frac{te^{\frac{t}{2}}+2e^{\frac{t}{2}}}{2}
Factor out \frac{1}{2}.
e^{\frac{t}{2}}\left(t+2\right)
Consider te^{\frac{1}{2}t}+2e^{\frac{1}{2}t}. Factor out e^{\frac{t}{2}}.
\frac{e^{\frac{t}{2}}\left(t+2\right)}{2}
Rewrite the complete factored expression.
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