Algebra Examples

$\frac{6}{k - 4} \div \frac{k + 6}{k^{2} + 2 k - 24}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{k - 4} \cdot \frac{k^{2} + 2 k - 24}{k + 6}$

Step 2

Factor $k^{2} + 2 k - 24$ using the AC method.

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Step 2.1

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 $- 24$ and whose sum is $2$ .

$- 4, 6$

Step 2.2

Write the factored form using these integers.

$\frac{6}{k - 4} \cdot \frac{(k - 4) (k + 6)}{k + 6}$

Step 3

Cancel the common factor of $k - 4$ .

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Step 3.1

Cancel the common factor.

$\frac{6}{k - 4} \cdot \frac{(k - 4) (k + 6)}{k + 6}$

Step 3.2

Rewrite the expression.

$6 \frac{k + 6}{k + 6}$

Step 4

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

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

Step 5

Cancel the common factor of $k + 6$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $6$ by $1$ .

$6$