Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Factor $5$ out of $10 m$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

Step 3.2

Multiply $2$ by $5$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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