Algebra Examples

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

Step 1

Multiply $\frac{3 \sqrt{b}}{\sqrt{b} + 2}$ by $\frac{\sqrt{b} - 2}{\sqrt{b} - 2}$ .

$\frac{3 \sqrt{b}}{\sqrt{b} + 2} \cdot \frac{\sqrt{b} - 2}{\sqrt{b} - 2}$

Step 2

Multiply $\frac{3 \sqrt{b}}{\sqrt{b} + 2}$ by $\frac{\sqrt{b} - 2}{\sqrt{b} - 2}$ .

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{(\sqrt{b} + 2) (\sqrt{b} - 2)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{{\sqrt{b}}^{2} + \sqrt{b} \cdot - 2 + 2 \sqrt{b} - 4}$

Step 4

Simplify.

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Step 4.1

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

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{{(b^{\frac{1}{2}})}^{2} - 4}$

Step 4.2

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

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{b^{\frac{1}{2} \cdot 2} - 4}$

Step 4.3

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

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{b^{\frac{2}{2}} - 4}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{b^{\frac{2}{2}} - 4}$

Step 4.4.2

Rewrite the expression.

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{b^{1} - 4}$

Step 4.5

Simplify.

$\frac{3 \sqrt{b} (\sqrt{b} - 2)}{b - 4}$

Step 5

Group $\sqrt{b} - 2$ and $\sqrt{b}$ together.

$\frac{3 ((\sqrt{b} - 2) \sqrt{b})}{b - 4}$

Step 6

Apply the distributive property.

$\frac{3 (\sqrt{b} \sqrt{b} - 2 \sqrt{b})}{b - 4}$

Step 7

Multiply $\sqrt{b} \sqrt{b}$ .

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Step 7.1

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

$\frac{3 ({\sqrt{b}}^{1} \sqrt{b} - 2 \sqrt{b})}{b - 4}$

Step 7.2

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

$\frac{3 ({\sqrt{b}}^{1} {\sqrt{b}}^{1} - 2 \sqrt{b})}{b - 4}$

Step 7.3

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

$\frac{3 ({\sqrt{b}}^{1 + 1} - 2 \sqrt{b})}{b - 4}$

Step 7.4

Add $1$ and $1$ .

$\frac{3 ({\sqrt{b}}^{2} - 2 \sqrt{b})}{b - 4}$

Step 8

Rewrite ${\sqrt{b}}^{2}$ as $b$ .

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Step 8.1

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

$\frac{3 ({(b^{\frac{1}{2}})}^{2} - 2 \sqrt{b})}{b - 4}$

Step 8.2

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

$\frac{3 (b^{\frac{1}{2} \cdot 2} - 2 \sqrt{b})}{b - 4}$

Step 8.3

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

$\frac{3 (b^{\frac{2}{2}} - 2 \sqrt{b})}{b - 4}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Cancel the common factor.

$\frac{3 (b^{\frac{2}{2}} - 2 \sqrt{b})}{b - 4}$

Step 8.4.2

Rewrite the expression.

$\frac{3 (b^{1} - 2 \sqrt{b})}{b - 4}$

Step 8.5

Simplify.

$\frac{3 (b - 2 \sqrt{b})}{b - 4}$

Step 9

Simplify the numerator.

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Step 9.1

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

$\frac{3 (b - 2 b^{\frac{1}{2}})}{b - 4}$

Step 9.2

Factor $b^{\frac{1}{2}}$ out of $b - 2 b^{\frac{1}{2}}$ .

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Step 9.2.1

Raise $b$ to the power of $1$ .

$\frac{3 (b^{1} - 2 b^{\frac{1}{2}})}{b - 4}$

Step 9.2.2

Factor $b^{\frac{1}{2}}$ out of $b^{1}$ .

$\frac{3 (b^{\frac{1}{2}} b^{\frac{1}{2}} - 2 b^{\frac{1}{2}})}{b - 4}$

Step 9.2.3

Factor $b^{\frac{1}{2}}$ out of $- 2 b^{\frac{1}{2}}$ .

$\frac{3 (b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} \cdot - 2)}{b - 4}$

Step 9.2.4

Factor $b^{\frac{1}{2}}$ out of $b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} \cdot - 2$ .

$\frac{3 (b^{\frac{1}{2}} (b^{\frac{1}{2}} - 2))}{b - 4}$

$\frac{3 b^{\frac{1}{2}} (b^{\frac{1}{2}} - 2)}{b - 4}$