Simplify ((30x+15)/x)÷(10/(3x))

$\frac{30 x + 15}{x} \div \frac{10}{3 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{30 x + 15}{x} \cdot \frac{3 x}{10}$

Step 2

Cancel the common factor of $x$ .

Factor $x$ out of $3 x$ .

$\frac{30 x + 15}{x} \cdot \frac{x \cdot 3}{10}$

Cancel the common factor.

$\frac{30 x + 15}{x} \cdot \frac{x \cdot 3}{10}$

Rewrite the expression.

$(30 x + 15) \frac{3}{10}$

Step 3

Apply the distributive property.

$30 x \frac{3}{10} + 15 (\frac{3}{10})$

Step 4

Cancel the common factor of $10$ .

Factor $10$ out of $30 x$ .

$10 (3 x) \frac{3}{10} + 15 (\frac{3}{10})$

Cancel the common factor.

$10 (3 x) \frac{3}{10} + 15 (\frac{3}{10})$

Rewrite the expression.

$3 x \cdot 3 + 15 (\frac{3}{10})$

Step 5

Multiply $3$ by $3$ .

$9 x + 15 (\frac{3}{10})$

Step 6

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$9 x + 5 (3) \frac{3}{10}$

Factor $5$ out of $10$ .

$9 x + 5 \cdot 3 \frac{3}{5 \cdot 2}$

Cancel the common factor.

$9 x + 5 \cdot 3 \frac{3}{5 \cdot 2}$

Rewrite the expression.

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

Step 7

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

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

Step 8

Multiply $3$ by $3$ .

$9 x + \frac{9}{2}$

Step 9

To write $9 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 x \cdot \frac{2}{2} + \frac{9}{2}$

Step 10

Simplify terms.

Combine $9 x$ and $\frac{2}{2}$ .

$\frac{9 x \cdot 2}{2} + \frac{9}{2}$

Combine the numerators over the common denominator.

$\frac{9 x \cdot 2 + 9}{2}$

Step 11

Simplify the numerator.

Factor $9$ out of $9 x \cdot 2 + 9$ .

Factor $9$ out of $9 x \cdot 2$ .

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

Factor $9$ out of $9$ .

$\frac{9 (x \cdot 2) + 9 (1)}{2}$

Factor $9$ out of $9 (x \cdot 2) + 9 (1)$ .

$\frac{9 (x \cdot 2 + 1)}{2}$

Move $2$ to the left of $x$ .

$\frac{9 (2 x + 1)}{2}$

Simplify ((30x+15)/x)÷(10/(3x))

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