Finite Math Examples

$\frac{8 x}{\sqrt{2 x + 6}}$

Step 1

Factor $2$ out of $2 x + 6$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{8 x}{\sqrt{2 (x) + 6}}$

Step 1.2

Factor $2$ out of $6$ .

$\frac{8 x}{\sqrt{2 x + 2 \cdot 3}}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 3$ .

$\frac{8 x}{\sqrt{2 (x + 3)}}$

Step 2

Multiply $\frac{8 x}{\sqrt{2 (x + 3)}}$ by $\frac{\sqrt{2 (x + 3)}}{\sqrt{2 (x + 3)}}$ .

$\frac{8 x}{\sqrt{2 (x + 3)}} \cdot \frac{\sqrt{2 (x + 3)}}{\sqrt{2 (x + 3)}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{8 x}{\sqrt{2 (x + 3)}}$ by $\frac{\sqrt{2 (x + 3)}}{\sqrt{2 (x + 3)}}$ .

$\frac{8 x \sqrt{2 (x + 3)}}{\sqrt{2 (x + 3)} \sqrt{2 (x + 3)}}$

Step 3.2

Raise $\sqrt{2 (x + 3)}$ to the power of $1$ .

$\frac{8 x \sqrt{2 (x + 3)}}{{\sqrt{2 (x + 3)}}^{1} \sqrt{2 (x + 3)}}$

Step 3.3

Raise $\sqrt{2 (x + 3)}$ to the power of $1$ .

$\frac{8 x \sqrt{2 (x + 3)}}{{\sqrt{2 (x + 3)}}^{1} {\sqrt{2 (x + 3)}}^{1}}$

Step 3.4

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

$\frac{8 x \sqrt{2 (x + 3)}}{{\sqrt{2 (x + 3)}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{8 x \sqrt{2 (x + 3)}}{{\sqrt{2 (x + 3)}}^{2}}$

Step 3.6

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

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Step 3.6.1

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

$\frac{8 x \sqrt{2 (x + 3)}}{{({(2 (x + 3))}^{\frac{1}{2}})}^{2}}$

Step 3.6.2

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

$\frac{8 x \sqrt{2 (x + 3)}}{{(2 (x + 3))}^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

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

$\frac{8 x \sqrt{2 (x + 3)}}{{(2 (x + 3))}^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\frac{8 x \sqrt{2 (x + 3)}}{{(2 (x + 3))}^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{8 x \sqrt{2 (x + 3)}}{{(2 (x + 3))}^{1}}$

Step 3.6.5

Simplify.

$\frac{8 x \sqrt{2 (x + 3)}}{2 (x + 3)}$

Step 4

Cancel the common factor of $8$ and $2$ .

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Step 4.1

Factor $2$ out of $8 x \sqrt{2 (x + 3)}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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