Simplify (5/(9x^2))÷(10/(3x))

$\frac{5}{9 x^{2}} \div \frac{10}{3 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{9 x^{2}} \cdot \frac{3 x}{10}$

Step 2

Combine.

$\frac{5 (3 x)}{9 x^{2} \cdot 10}$

Step 3

Cancel the common factors.

Factor $5$ out of $9 x^{2} \cdot 10$ .

$\frac{5 (3 x)}{5 (9 x^{2} \cdot 2)}$

Cancel the common factor.

$\frac{5 (3 x)}{5 (9 x^{2} \cdot 2)}$

Rewrite the expression.

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

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

Step 4

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x)}{9 x^{2} \cdot 2}$

Cancel the common factors.

Factor $3$ out of $9 x^{2} \cdot 2$ .

$\frac{3 (x)}{3 (3 x^{2} \cdot 2)}$

Cancel the common factor.

$\frac{3 x}{3 (3 x^{2} \cdot 2)}$

Rewrite the expression.

$\frac{x}{3 x^{2} \cdot 2}$

$\frac{x}{3 x^{2} \cdot 2}$

$\frac{x}{3 x^{2} \cdot 2}$

Step 5

Cancel the common factor of $x$ and $x^{2}$ .

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

$\frac{x^{1}}{3 x^{2} \cdot 2}$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1}{3 x^{2} \cdot 2}$

Cancel the common factors.

Factor $x$ out of $3 x^{2} \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3 x \cdot 2}$

$\frac{1}{3 x \cdot 2}$

$\frac{1}{3 x \cdot 2}$

Step 6

Multiply $2$ by $3$ .

$\frac{1}{6 x}$

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