Basic Math Examples

$\frac{n^{2} - n}{n^{2} - 1} \div \frac{n + 6}{n^{2} + 7 n + 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{n^{2} - n}{n^{2} - 1} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 2

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

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Step 2.1

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

$\frac{n \cdot n - n}{n^{2} - 1} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 2.2

Factor $n$ out of $- n$ .

$\frac{n \cdot n + n \cdot - 1}{n^{2} - 1} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 2.3

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

$\frac{n (n - 1)}{n^{2} - 1} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{n (n - 1)}{n^{2} - 1^{2}} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

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 $a = n$ and $b = 1$ .

$\frac{n (n - 1)}{(n + 1) (n - 1)} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 4

Cancel the common factor of $n - 1$ .

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Step 4.1

Cancel the common factor.

$\frac{n (n - 1)}{(n + 1) (n - 1)} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 4.2

Rewrite the expression.

$\frac{n}{n + 1} \cdot \frac{n^{2} + 7 n + 6}{n + 6}$

Step 5

Factor $n^{2} + 7 n + 6$ 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 $6$ and whose sum is $7$ .

$1, 6$

Step 5.2

Write the factored form using these integers.

$\frac{n}{n + 1} \cdot \frac{(n + 1) (n + 6)}{n + 6}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $n + 1$ .

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Step 6.1.1

Cancel the common factor.

$\frac{n}{n + 1} \cdot \frac{(n + 1) (n + 6)}{n + 6}$

Step 6.1.2

Rewrite the expression.

$n \frac{n + 6}{n + 6}$

Step 6.2

Combine $n$ and $\frac{n + 6}{n + 6}$ .

$\frac{n (n + 6)}{n + 6}$

Step 6.3

Cancel the common factor of $n + 6$ .

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Step 6.3.1

Cancel the common factor.

$\frac{n (n + 6)}{n + 6}$

Step 6.3.2

Divide $n$ by $1$ .

$n$