Algebra Examples

$\frac{m a - m b}{3 n^{2}} \cdot \frac{2 m}{n b - n a}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $m$ out of $m a - m b$ .

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Step 1.1.1

Factor $m$ out of $m a$ .

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

Step 1.1.2

Factor $m$ out of $- m b$ .

$\frac{m (a) + m (- 1 b)}{3 n^{2}} \cdot \frac{2 m}{n b - n a}$

Step 1.1.3

Factor $m$ out of $m (a) + m (- 1 b)$ .

$\frac{m (a - 1 b)}{3 n^{2}} \cdot \frac{2 m}{n b - n a}$

Step 1.2

Rewrite $- 1 b$ as $- b$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Factor $n$ out of $n b - n a$ .

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Step 2.1.1

Factor $n$ out of $n b$ .

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

Step 2.1.2

Factor $n$ out of $- n a$ .

$\frac{m (a - b)}{3 n^{2}} \cdot \frac{2 m}{n (b) + n (- 1 a)}$

Step 2.1.3

Factor $n$ out of $n (b) + n (- 1 a)$ .

$\frac{m (a - b)}{3 n^{2}} \cdot \frac{2 m}{n (b - 1 a)}$

Step 2.2

Rewrite $- 1 a$ as $- a$ .

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

Step 3

Combine.

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

Step 4

Multiply $m$ by $m$ by adding the exponents.

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Step 4.1

Move $m$ .

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

Step 4.2

Multiply $m$ by $m$ .

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

Step 5

Multiply $n^{2}$ by $n$ by adding the exponents.

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Step 5.1

Move $n$ .

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

Step 5.2

Multiply $n$ by $n^{2}$ .

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Step 5.2.1

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

$\frac{m^{2} (a - b) \cdot 2}{3 (n^{1} n^{2}) (b - a)}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m^{2} (a - b) \cdot 2}{3 n^{1 + 2} (b - a)}$

Step 5.3

Add $1$ and $2$ .

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

Step 6

Cancel the common factor of $a - b$ and $b - a$ .

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Step 6.1

Factor $- 1$ out of $a$ .

$\frac{m^{2} (- 1 (- a) - b) \cdot 2}{3 n^{3} (b - a)}$

Step 6.2

Factor $- 1$ out of $- b$ .

$\frac{m^{2} (- 1 (- a) - (b)) \cdot 2}{3 n^{3} (b - a)}$

Step 6.3

Factor $- 1$ out of $- 1 (- a) - (b)$ .

$\frac{m^{2} (- 1 (- a + b)) \cdot 2}{3 n^{3} (b - a)}$

Step 6.4

Reorder terms.

$\frac{m^{2} (- 1 (- a + b)) \cdot 2}{3 n^{3} (- a + b)}$

Step 6.5

Cancel the common factor.

$\frac{m^{2} (- 1 (- a + b)) \cdot 2}{3 n^{3} (- a + b)}$

Step 6.6

Rewrite the expression.

$\frac{m^{2} \cdot (- 1) \cdot 2}{3 n^{3}}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $2$ by $- 1$ .

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

Step 7.2

Move $- 2$ to the left of $m^{2}$ .

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

Step 7.3

Move the negative in front of the fraction.

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