Simplify ((14x+7)/x)÷(21/(2x))

$\frac{14 x + 7}{x} \div \frac{21}{2 x}$

To divide by a fraction, multiply by its reciprocal.

$\frac{14 x + 7}{x} \cdot \frac{2 x}{21}$

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{14 x + 7}{x} \cdot \frac{x \cdot 2}{21}$

Cancel the common factor.

$\frac{14 x + 7}{x} \cdot \frac{x \cdot 2}{21}$

Rewrite the expression.

$(14 x + 7) \frac{2}{21}$

$(14 x + 7) \frac{2}{21}$

Apply the distributive property.

$14 x \frac{2}{21} + 7 (\frac{2}{21})$

Cancel the common factor of $7$ .

Factor $7$ out of $14 x$ .

$7 (2 x) \frac{2}{21} + 7 (\frac{2}{21})$

Factor $7$ out of $21$ .

$7 (2 x) \frac{2}{7 (3)} + 7 (\frac{2}{21})$

Cancel the common factor.

$7 (2 x) \frac{2}{7 \cdot 3} + 7 (\frac{2}{21})$

Rewrite the expression.

$2 x \frac{2}{3} + 7 (\frac{2}{21})$

$2 x \frac{2}{3} + 7 (\frac{2}{21})$

Combine $2$ and $\frac{2}{3}$ .

$x \frac{2 \cdot 2}{3} + 7 (\frac{2}{21})$

Multiply $2$ by $2$ .

$x \frac{4}{3} + 7 (\frac{2}{21})$

Combine $x$ and $\frac{4}{3}$ .

$\frac{x \cdot 4}{3} + 7 (\frac{2}{21})$

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

$\frac{x \cdot 4}{3} + 7 \frac{2}{7 (3)}$

Cancel the common factor.

$\frac{x \cdot 4}{3} + 7 \frac{2}{7 \cdot 3}$

Rewrite the expression.

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

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

Combine the numerators over the common denominator.

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

Reorder factors in $x \cdot 4 + 2$ .

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

Factor $2$ out of $4 x + 2$ .

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (2 x) + 2 (1)$ .

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

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

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