Algebra Examples

$\frac{3}{2} x^{\frac{1}{2}} + \frac{5}{2} x^{\frac{3}{2}}$

Step 1

Factor $x^{\frac{1}{2}}$ out of $\frac{3}{2} x^{\frac{1}{2}} + \frac{5}{2} x^{\frac{3}{2}}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Reorder $\frac{3}{2}$ and $x^{\frac{1}{2}}$ .

$x^{\frac{1}{2}} \frac{3}{2} + \frac{5}{2} x^{\frac{3}{2}}$

Step 1.1.2

Reorder $\frac{5}{2}$ and $x^{\frac{3}{2}}$ .

$x^{\frac{1}{2}} \frac{3}{2} + x^{\frac{3}{2}} \frac{5}{2}$

Step 1.2

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{3}{2}} \frac{5}{2}$ .

$x^{\frac{1}{2}} (\frac{3}{2}) + x^{\frac{1}{2}} (x^{\frac{2}{2}} \frac{5}{2})$

Step 1.3

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{1}{2}} (\frac{3}{2}) + x^{\frac{1}{2}} (x^{\frac{2}{2}} \frac{5}{2})$ .

$x^{\frac{1}{2}} (\frac{3}{2} + x^{\frac{2}{2}} \frac{5}{2})$

Step 2

Divide $2$ by $2$ .

$x^{\frac{1}{2}} (\frac{3}{2} + x^{1} \frac{5}{2})$

Step 3

Simplify.

$x^{\frac{1}{2}} (\frac{3}{2} + x \frac{5}{2})$

Step 4

Combine $x$ and $\frac{5}{2}$ .

$x^{\frac{1}{2}} (\frac{3}{2} + \frac{x \cdot 5}{2})$

Step 5

Move $5$ to the left of $x$ .

$x^{\frac{1}{2}} (\frac{3}{2} + \frac{5 \cdot x}{2})$

Step 6

Multiply $5$ by $x$ .

$x^{\frac{1}{2}} (\frac{3}{2} + \frac{5 x}{2})$