Simplify (10m-15n)÷(((2m-3n)^2)/(2m))

$(10 m - 15 n) \div \frac{{(2 m - 3 n)}^{2}}{2 m}$

To divide by a fraction, multiply by its reciprocal.

$(10 m - 15 n) \frac{2 m}{{(2 m - 3 n)}^{2}}$

Multiply $10 m - 15 n$ by $\frac{2 m}{{(2 m - 3 n)}^{2}}$ .

$\frac{(10 m - 15 n) (2 m)}{{(2 m - 3 n)}^{2}}$

Simplify the numerator.

Factor $5$ out of $10 m - 15 n$ .

Factor $5$ out of $10 m$ .

$\frac{(5 (2 m) - 15 n) \cdot 2 m}{{(2 m - 3 n)}^{2}}$

Factor $5$ out of $- 15 n$ .

$\frac{(5 (2 m) + 5 (- 3 n)) \cdot 2 m}{{(2 m - 3 n)}^{2}}$

Factor $5$ out of $5 (2 m) + 5 (- 3 n)$ .

$\frac{5 (2 m - 3 n) \cdot 2 m}{{(2 m - 3 n)}^{2}}$

Multiply $2$ by $5$ .

$\frac{10 (2 m - 3 n) m}{{(2 m - 3 n)}^{2}}$

Cancel the common factor of $2 m - 3 n$ and ${(2 m - 3 n)}^{2}$ .

Factor $2 m - 3 n$ out of $10 (2 m - 3 n) m$ .

$\frac{(2 m - 3 n) (10 m)}{{(2 m - 3 n)}^{2}}$

Cancel the common factors.

Factor $2 m - 3 n$ out of ${(2 m - 3 n)}^{2}$ .

$\frac{(2 m - 3 n) (10 m)}{(2 m - 3 n) (2 m - 3 n)}$

Cancel the common factor.

$\frac{(2 m - 3 n) (10 m)}{(2 m - 3 n) (2 m - 3 n)}$

Rewrite the expression.

$\frac{10 m}{2 m - 3 n}$