Pre-Algebra Examples

$\frac{x + 5}{x - 8} \div \frac{x + 4}{x^{2} - 5 x - 24}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 5}{x - 8} \cdot \frac{x^{2} - 5 x - 24}{x + 4}$

Step 2

Factor $x^{2} - 5 x - 24$ 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 $- 5$ .

$- 8, 3$

Step 2.2

Write the factored form using these integers.

$\frac{x + 5}{x - 8} \cdot \frac{(x - 8) (x + 3)}{x + 4}$

Step 3

Cancel the common factor of $x - 8$ .

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Step 3.1

Cancel the common factor.

$\frac{x + 5}{x - 8} \cdot \frac{(x - 8) (x + 3)}{x + 4}$

Step 3.2

Rewrite the expression.

$(x + 5) \frac{x + 3}{x + 4}$

Step 4

Multiply $x + 5$ by $\frac{x + 3}{x + 4}$ .

$\frac{(x + 5) (x + 3)}{x + 4}$