Basic Math Examples

$\frac{8 - k}{k^{2} - 64} \div \frac{k - 8}{k + 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 - k}{k^{2} - 64} \cdot \frac{k + 8}{k - 8}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$\frac{8 - k}{k^{2} - 8^{2}} \cdot \frac{k + 8}{k - 8}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = k$ and $b = 8$ .

$\frac{8 - k}{(k + 8) (k - 8)} \cdot \frac{k + 8}{k - 8}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $k + 8$ .

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Step 3.1.1

Cancel the common factor.

$\frac{8 - k}{(k + 8) (k - 8)} \cdot \frac{k + 8}{k - 8}$

Step 3.1.2

Rewrite the expression.

$\frac{8 - k}{k - 8} \cdot \frac{1}{k - 8}$

Step 3.2

Multiply $\frac{8 - k}{k - 8}$ by $\frac{1}{k - 8}$ .

$\frac{8 - k}{(k - 8) (k - 8)}$

Step 4

Raise $k - 8$ to the power of $1$ .

$\frac{8 - k}{{(k - 8)}^{1} (k - 8)}$

Step 5

Raise $k - 8$ to the power of $1$ .

$\frac{8 - k}{{(k - 8)}^{1} {(k - 8)}^{1}}$

Step 6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 - k}{{(k - 8)}^{1 + 1}}$

Step 7

Add $1$ and $1$ .

$\frac{8 - k}{{(k - 8)}^{2}}$

Step 8

Cancel the common factor of $8 - k$ and ${(k - 8)}^{2}$ .

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Step 8.1

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- 1 (- 8) - k}{{(k - 8)}^{2}}$

Step 8.2

Factor $- 1$ out of $- k$ .

$\frac{- 1 (- 8) - (k)}{{(k - 8)}^{2}}$

Step 8.3

Factor $- 1$ out of $- 1 (- 8) - (k)$ .

$\frac{- 1 (- 8 + k)}{{(k - 8)}^{2}}$

Step 8.4

Reorder terms.

$\frac{- 1 (k - 8)}{{(k - 8)}^{2}}$

Step 8.5

Factor $k - 8$ out of $- 1 (k - 8)$ .

$\frac{(k - 8) \cdot - 1}{{(k - 8)}^{2}}$

Step 8.6

Cancel the common factors.

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Step 8.6.1

Factor $k - 8$ out of ${(k - 8)}^{2}$ .

$\frac{(k - 8) \cdot - 1}{(k - 8) (k - 8)}$

Step 8.6.2

Cancel the common factor.

$\frac{(k - 8) \cdot - 1}{(k - 8) (k - 8)}$

Step 8.6.3

Rewrite the expression.

$\frac{- 1}{k - 8}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{k - 8}$