Algebra Examples

$\frac{10 \sqrt{12} - 4 \sqrt{12}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$\frac{10 \sqrt{4 (3)} - 4 \sqrt{12}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.1.2

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

$\frac{10 \sqrt{2^{2} \cdot 3} - 4 \sqrt{12}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.2

Pull terms out from under the radical.

$\frac{10 (2 \sqrt{3}) - 4 \sqrt{12}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.3

Multiply $2$ by $10$ .

$\frac{20 \sqrt{3} - 4 \sqrt{12}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$\frac{20 \sqrt{3} - 4 \sqrt{4 (3)}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.4.2

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

$\frac{20 \sqrt{3} - 4 \sqrt{2^{2} \cdot 3}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.5

Pull terms out from under the radical.

$\frac{20 \sqrt{3} - 4 (2 \sqrt{3})}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.6

Multiply $2$ by $- 4$ .

$\frac{20 \sqrt{3} - 8 \sqrt{3}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 1.7

Subtract $8 \sqrt{3}$ from $20 \sqrt{3}$ .

$\frac{12 \sqrt{3}}{20 \sqrt{3} + 30 \sqrt{3}}$

Step 2

Simplify terms.

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Step 2.1

Add $20 \sqrt{3}$ and $30 \sqrt{3}$ .

$\frac{12 \sqrt{3}}{50 \sqrt{3}}$

Step 2.2

Cancel the common factor of $12$ and $50$ .

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Step 2.2.1

Factor $2$ out of $12 \sqrt{3}$ .

$\frac{2 (6 \sqrt{3})}{50 \sqrt{3}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $50 \sqrt{3}$ .

$\frac{2 (6 \sqrt{3})}{2 (25 \sqrt{3})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 (6 \sqrt{3})}{2 (25 \sqrt{3})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{6 \sqrt{3}}{25 \sqrt{3}}$

Step 2.3

Cancel the common factor of $\sqrt{3}$ .

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Step 2.3.1

Cancel the common factor.

$\frac{6 \sqrt{3}}{25 \sqrt{3}}$

Step 2.3.2

Rewrite the expression.

$\frac{6}{25}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{25}$

Decimal Form:

$0.24$