Algebra Examples

$\frac{2 x}{27} \div \frac{4 x + 20}{9}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x}{27} \cdot \frac{9}{4 x + 20}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $9$ .

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Step 2.1.1

Factor $9$ out of $27$ .

$\frac{2 x}{9 (3)} \cdot \frac{9}{4 x + 20}$

Step 2.1.2

Cancel the common factor.

$\frac{2 x}{9 \cdot 3} \cdot \frac{9}{4 x + 20}$

Step 2.1.3

Rewrite the expression.

$\frac{2 x}{3} \cdot \frac{1}{4 x + 20}$

$\frac{2 x}{3} \cdot \frac{1}{4 x + 20}$

Step 2.2

Multiply $\frac{2 x}{3}$ by $\frac{1}{4 x + 20}$ .

$\frac{2 x}{3 (4 x + 20)}$

Step 2.3

Cancel the common factor of $2$ and $4 x + 20$ .

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Step 2.3.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{3 (4 x + 20)}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $3 (4 x + 20)$ .

$\frac{2 (x)}{2 (3 (2 x + 10))}$

Step 2.3.2.2

Cancel the common factor.

$\frac{2 x}{2 (3 (2 x + 10))}$

Step 2.3.2.3

Rewrite the expression.

$\frac{x}{3 (2 x + 10)}$

$\frac{x}{3 (2 x + 10)}$

$\frac{x}{3 (2 x + 10)}$

$\frac{x}{3 (2 x + 10)}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $2$ out of $2 x + 10$ .

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Step 3.1.1

Factor $2$ out of $2 x$ .

$\frac{x}{3 (2 (x) + 10)}$

Step 3.1.2

Factor $2$ out of $10$ .

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

Step 3.1.3

Factor $2$ out of $2 x + 2 \cdot 5$ .

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

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

Step 3.2

Multiply $3$ by $2$ .

$\frac{x}{6 (x + 5)}$

$\frac{x}{6 (x + 5)}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$