Basic Math Examples

$\frac{n^{2} - 49}{8 n + 56} \cdot \frac{8}{7 - n}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $49$ as $7^{2}$ .

$\frac{n^{2} - 7^{2}}{8 n + 56} \cdot \frac{8}{7 - n}$

Step 1.2

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 $b = 7$ .

$\frac{(n + 7) (n - 7)}{8 n + 56} \cdot \frac{8}{7 - n}$

Step 2

Simplify terms.

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Step 2.1

Factor $8$ out of $8 n + 56$ .

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Step 2.1.1

Factor $8$ out of $8 n$ .

$\frac{(n + 7) (n - 7)}{8 (n) + 56} \cdot \frac{8}{7 - n}$

Step 2.1.2

Factor $8$ out of $56$ .

$\frac{(n + 7) (n - 7)}{8 n + 8 \cdot 7} \cdot \frac{8}{7 - n}$

Step 2.1.3

Factor $8$ out of $8 n + 8 \cdot 7$ .

$\frac{(n + 7) (n - 7)}{8 (n + 7)} \cdot \frac{8}{7 - n}$

Step 2.2

Cancel the common factor of $8$ .

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Step 2.2.1

Cancel the common factor.

$\frac{(n + 7) (n - 7)}{8 (n + 7)} \cdot \frac{8}{7 - n}$

Step 2.2.2

Rewrite the expression.

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

Step 2.3

Multiply $\frac{(n + 7) (n - 7)}{n + 7}$ by $\frac{1}{7 - n}$ .

$\frac{(n + 7) (n - 7)}{(n + 7) (7 - n)}$

Step 2.4

Cancel the common factor of $n + 7$ .

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Step 2.4.1

Cancel the common factor.

$\frac{(n + 7) (n - 7)}{(n + 7) (7 - n)}$

Step 2.4.2

Rewrite the expression.

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

Step 2.5

Cancel the common factor of $n - 7$ and $7 - n$ .

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Step 2.5.1

Factor $- 1$ out of $n$ .

$\frac{- 1 (- n) - 7}{7 - n}$

Step 2.5.2

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{- 1 (- n) - 1 (7)}{7 - n}$

Step 2.5.3

Factor $- 1$ out of $- 1 (- n) - 1 (7)$ .

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

Step 2.5.4

Reorder terms.

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

Step 2.5.5

Cancel the common factor.

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

Step 2.5.6

Divide $- 1$ by $1$ .

$- 1$