Pre-Algebra Examples

$\frac{\frac{12 m^{2} n^{5}}{3 m^{3} n}}{\frac{m + 5}{m^{2} - 25}}$

Step 1

Cancel the common factor of $12$ and $3$ .

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Step 1.1

Factor $3$ out of $12 m^{2} n^{5}$ .

$\frac{\frac{3 (4 m^{2} n^{5})}{3 m^{3} n}}{\frac{m + 5}{m^{2} - 25}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3 m^{3} n$ .

$\frac{\frac{3 (4 m^{2} n^{5})}{3 (m^{3} n)}}{\frac{m + 5}{m^{2} - 25}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{3 (4 m^{2} n^{5})}{3 (m^{3} n)}}{\frac{m + 5}{m^{2} - 25}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{4 m^{2} n^{5}}{m^{3} n}}{\frac{m + 5}{m^{2} - 25}}$

Step 2

Cancel the common factor of $m^{2}$ and $m^{3}$ .

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Step 2.1

Factor $m^{2}$ out of $4 m^{2} n^{5}$ .

$\frac{\frac{m^{2} (4 n^{5})}{m^{3} n}}{\frac{m + 5}{m^{2} - 25}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{\frac{m^{2} (4 n^{5})}{m^{2} (m n)}}{\frac{m + 5}{m^{2} - 25}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{m^{2} (4 n^{5})}{m^{2} (m n)}}{\frac{m + 5}{m^{2} - 25}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{4 n^{5}}{m n}}{\frac{m + 5}{m^{2} - 25}}$

Step 3

Cancel the common factor of $n^{5}$ and $n$ .

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Step 3.1

Factor $n$ out of $4 n^{5}$ .

$\frac{\frac{n (4 n^{4})}{m n}}{\frac{m + 5}{m^{2} - 25}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $n$ out of $m n$ .

$\frac{\frac{n (4 n^{4})}{n m}}{\frac{m + 5}{m^{2} - 25}}$

Step 3.2.2

Cancel the common factor.

$\frac{\frac{n (4 n^{4})}{n m}}{\frac{m + 5}{m^{2} - 25}}$

Step 3.2.3

Rewrite the expression.

$\frac{\frac{4 n^{4}}{m}}{\frac{m + 5}{m^{2} - 25}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4 n^{4}}{m} \cdot \frac{m^{2} - 25}{m + 5}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $25$ as $5^{2}$ .

$\frac{4 n^{4}}{m} \cdot \frac{m^{2} - 5^{2}}{m + 5}$

Step 5.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 5$ .

$\frac{4 n^{4}}{m} \cdot \frac{(m + 5) (m - 5)}{m + 5}$

Step 6

Cancel the common factor of $m + 5$ .

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Step 6.1

Cancel the common factor.

$\frac{4 n^{4}}{m} \cdot \frac{(m + 5) (m - 5)}{m + 5}$

Step 6.2

Divide $m - 5$ by $1$ .

$\frac{4 n^{4}}{m} (m - 5)$

Step 7

Multiply $\frac{4 n^{4}}{m}$ by $m - 5$ .

$\frac{4 n^{4} (m - 5)}{m}$

Step 8

Apply the distributive property.

$\frac{4 n^{4} m + 4 n^{4} \cdot - 5}{m}$

Step 9

Multiply $- 5$ by $4$ .

$\frac{4 n^{4} m - 20 n^{4}}{m}$

Step 10

Split the fraction $\frac{4 n^{4} m - 20 n^{4}}{m}$ into two fractions.

$\frac{4 n^{4} m}{m} + \frac{- 20 n^{4}}{m}$

Step 11

Cancel the common factor of $m$ .

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Step 11.1

Cancel the common factor.

$\frac{4 n^{4} m}{m} + \frac{- 20 n^{4}}{m}$

Step 11.2

Divide $4 n^{4}$ by $1$ .

$4 n^{4} + \frac{- 20 n^{4}}{m}$

Step 12

Move the negative in front of the fraction.

$4 n^{4} - \frac{20 n^{4}}{m}$