Basic Math Examples

$\frac{n - 1}{n + 8} \cdot \frac{n^{2} + 5 n - 24}{n - 1}$

Step 1

Factor $n^{2} + 5 n - 24$ using the AC method.

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Step 1.1

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 $5$ .

$- 3, 8$

Step 1.2

Write the factored form using these integers.

$\frac{n - 1}{n + 8} \cdot \frac{(n - 3) (n + 8)}{n - 1}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $n - 1$ .

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Step 2.1.1

Cancel the common factor.

$\frac{n - 1}{n + 8} \cdot \frac{(n - 3) (n + 8)}{n - 1}$

Step 2.1.2

Rewrite the expression.

$\frac{1}{n + 8} \cdot ((n - 3) (n + 8))$

Step 2.2

Cancel the common factor of $n + 8$ .

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Step 2.2.1

Factor $n + 8$ out of $(n - 3) (n + 8)$ .

$\frac{1}{n + 8} \cdot ((n + 8) (n - 3))$

Step 2.2.2

Cancel the common factor.

$\frac{1}{n + 8} \cdot ((n + 8) (n - 3))$

Step 2.2.3

Rewrite the expression.

$n - 3$