Pre-Algebra Examples

$\frac{n + 1}{4 n^{2}} \div \frac{(n - 1) (n + 1)}{4 n^{2} (n + 7)}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{n + 1}{4 n^{2}} \cdot \frac{4 n^{2} (n + 7)}{(n - 1) (n + 1)}$

Step 2

Cancel the common factor of $n + 1$ .

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Step 2.1

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

$\frac{n + 1}{4 n^{2}} \cdot \frac{4 n^{2} (n + 7)}{(n + 1) (n - 1)}$

Step 2.2

Cancel the common factor.

$\frac{n + 1}{4 n^{2}} \cdot \frac{4 n^{2} (n + 7)}{(n + 1) (n - 1)}$

Step 2.3

Rewrite the expression.

$\frac{1}{4 n^{2}} \cdot \frac{4 n^{2} (n + 7)}{n - 1}$

Step 3

Cancel the common factor of $4 n^{2}$ .

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Step 3.1

Cancel the common factor.

$\frac{1}{4 n^{2}} \cdot \frac{4 n^{2} (n + 7)}{n - 1}$

Step 3.2

Rewrite the expression.

$\frac{n + 7}{n - 1}$