Algebra Examples

$\frac{4}{\sqrt{12 x}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$\frac{4}{\sqrt{4 (3) x}}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{4}{\sqrt{2^{2} \cdot 3 x}}$

Step 1.1.3

Add parentheses.

$\frac{4}{\sqrt{2^{2} \cdot (3 x)}}$

Step 1.2

Pull terms out from under the radical.

$\frac{4}{2 \sqrt{3 x}}$

Step 2

Cancel the common factor of $4$ and $2$ .

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Step 2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 2}{2 \sqrt{3 x}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 \sqrt{3 x}$ .

$\frac{2 \cdot 2}{2 (\sqrt{3 x})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 2}{2 \sqrt{3 x}}$

Step 2.2.3

Rewrite the expression.

$\frac{2}{\sqrt{3 x}}$

Step 3

Multiply $\frac{2}{\sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

$\frac{2}{\sqrt{3 x}} \cdot \frac{\sqrt{3 x}}{\sqrt{3 x}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{2}{\sqrt{3 x}}$ by $\frac{\sqrt{3 x}}{\sqrt{3 x}}$ .

$\frac{2 \sqrt{3 x}}{\sqrt{3 x} \sqrt{3 x}}$

Step 4.2

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{2 \sqrt{3 x}}{{\sqrt{3 x}}^{1} \sqrt{3 x}}$

Step 4.3

Raise $\sqrt{3 x}$ to the power of $1$ .

$\frac{2 \sqrt{3 x}}{{\sqrt{3 x}}^{1} {\sqrt{3 x}}^{1}}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.5

Add $1$ and $1$ .

$\frac{2 \sqrt{3 x}}{{\sqrt{3 x}}^{2}}$

Step 4.6

Rewrite ${\sqrt{3 x}}^{2}$ as $3 x$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x}$ as ${(3 x)}^{\frac{1}{2}}$ .

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

Step 4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.6.3

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

$\frac{2 \sqrt{3 x}}{{(3 x)}^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{2 \sqrt{3 x}}{{(3 x)}^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

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

Step 4.6.5

Simplify.

$\frac{2 \sqrt{3 x}}{3 x}$