# Laplace transform of 1+2sqrt t+3/sqrt t

Laplace transform of

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In problems 21.1

2.  Simplify each term.

$1+2\sqrt{t}+\frac{3\sqrt{t}}{t}$

$\frac{t+3\sqrt{t}}{t}+2\sqrt{t}$

$\frac{{t}^{\frac{1}{2}}+3}{{t}^{\frac{1}{2}}}+2\sqrt{t}$

multiply by $\frac{{t}^{\frac{1}{2}}}{{t}^{\frac{1}{2}}}$.

$\frac{{t}^{\frac{1}{2}}+3}{{t}^{\frac{1}{2}}}+\frac{2\sqrt{t}{t}^{\frac{1}{2}}}{{t}^{\frac{1}{2}}}$

$\frac{{t}^{\frac{1}{2}}+3+2\sqrt{t}{t}^{\frac{1}{2}}}{{t}^{\frac{1}{2}}}$

Simplify the numerator.

$\frac{2t+{t}^{\frac{1}{2}}+3}{{t}^{\frac{1}{2}}}$