Precalculus Examples

$3 x^{- \frac{1}{2}} + \frac{3}{2} x^{\frac{1}{2}}$

Step 1

Factor $\frac{1}{2}$ out of each term.

$\frac{1}{2} (\frac{6}{x^{\frac{1}{2}}} + 3 x^{\frac{1}{2}})$

Step 2

Factor.

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Step 2.1

Factor $3$ out of $\frac{6}{x^{\frac{1}{2}}} + 3 x^{\frac{1}{2}}$ .

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Step 2.1.1

Factor $3$ out of $\frac{6}{x^{\frac{1}{2}}}$ .

$\frac{1}{2} \cdot (3 \frac{2}{x^{\frac{1}{2}}} + 3 x^{\frac{1}{2}})$

Step 2.1.2

Factor $3$ out of $3 \frac{2}{x^{\frac{1}{2}}} + 3 x^{\frac{1}{2}}$ .

$\frac{1}{2} \cdot (3 (\frac{2}{x^{\frac{1}{2}}} + x^{\frac{1}{2}}))$

Step 2.2

Remove unnecessary parentheses.

$\frac{1}{2} \cdot 3 (\frac{2}{x^{\frac{1}{2}}} + x^{\frac{1}{2}})$

Step 3

Combine $\frac{1}{2}$ and $3$ .

$\frac{3}{2} (\frac{2}{x^{\frac{1}{2}}} + x^{\frac{1}{2}})$