Divide ((5x)/8)÷((15x^2)/4)

$\frac{5 x}{8} \div \frac{15 x^{2}}{4}$

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x}{8} \cdot \frac{4}{15 x^{2}}$

Combine.

$\frac{5 x \cdot 4}{8 (15 x^{2})}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5 x \cdot 4$ .

$\frac{5 (x \cdot 4)}{8 (15 x^{2})}$

Cancel the common factors.

Factor $5$ out of $8 (15 x^{2})$ .

$\frac{5 (x \cdot 4)}{5 (8 (3 x^{2}))}$

Cancel the common factor.

$\frac{5 (x \cdot 4)}{5 (8 (3 x^{2}))}$

Rewrite the expression.

$\frac{x \cdot 4}{8 (3 x^{2})}$

$\frac{x \cdot 4}{8 (3 x^{2})}$

$\frac{x \cdot 4}{8 (3 x^{2})}$

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

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4)}{8 (3 x^{2})}$

Cancel the common factors.

Factor $x$ out of $8 (3 x^{2})$ .

$\frac{x (4)}{x (8 (3 x))}$

Cancel the common factor.

$\frac{x \cdot 4}{x (8 (3 x))}$

Rewrite the expression.

$\frac{4}{8 (3 x)}$

$\frac{4}{8 (3 x)}$

$\frac{4}{8 (3 x)}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$\frac{4 (1)}{8 (3 x)}$

Cancel the common factors.

Factor $4$ out of $8 (3 x)$ .

$\frac{4 (1)}{4 (2 (3 x))}$

Cancel the common factor.

$\frac{4 \cdot 1}{4 (2 (3 x))}$

Rewrite the expression.

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

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

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

Multiply $2$ by $3$ .

$\frac{1}{6 x}$

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