Basic Math Examples

$\frac{m^{2} - m}{m^{2} - 1} \div \frac{m + 11}{m^{2} + 12 m + 11}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{m^{2} - m}{m^{2} - 1} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 2

Factor $m$ out of $m^{2} - m$ .

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Step 2.1

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

$\frac{m \cdot m - m}{m^{2} - 1} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 2.2

Factor $m$ out of $- m$ .

$\frac{m \cdot m + m \cdot - 1}{m^{2} - 1} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 2.3

Factor $m$ out of $m \cdot m + m \cdot - 1$ .

$\frac{m (m - 1)}{m^{2} - 1} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

$\frac{m (m - 1)}{m^{2} - 1^{2}} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 3.2

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 $b = 1$ .

$\frac{m (m - 1)}{(m + 1) (m - 1)} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 4

Cancel the common factor of $m - 1$ .

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Step 4.1

Cancel the common factor.

$\frac{m (m - 1)}{(m + 1) (m - 1)} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 4.2

Rewrite the expression.

$\frac{m}{m + 1} \cdot \frac{m^{2} + 12 m + 11}{m + 11}$

Step 5

Factor $m^{2} + 12 m + 11$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $11$ and whose sum is $12$ .

$1, 11$

Step 5.2

Write the factored form using these integers.

$\frac{m}{m + 1} \cdot \frac{(m + 1) (m + 11)}{m + 11}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $m + 1$ .

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Step 6.1.1

Cancel the common factor.

$\frac{m}{m + 1} \cdot \frac{(m + 1) (m + 11)}{m + 11}$

Step 6.1.2

Rewrite the expression.

$m \frac{m + 11}{m + 11}$

Step 6.2

Combine $m$ and $\frac{m + 11}{m + 11}$ .

$\frac{m (m + 11)}{m + 11}$

Step 6.3

Cancel the common factor of $m + 11$ .

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Step 6.3.1

Cancel the common factor.

$\frac{m (m + 11)}{m + 11}$

Step 6.3.2

Divide $m$ by $1$ .

$m$