Finite Math Examples

$\frac{x^{2} - 6 x - 40}{x^{2} - 8 x - 20} \cdot \frac{x + 7}{x + 4}$

Step 1

Factor $x^{2} - 6 x - 40$ 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 $- 40$ and whose sum is $- 6$ .

$- 10, 4$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 10) (x + 4)}{x^{2} - 8 x - 20} \cdot \frac{x + 7}{x + 4}$

Step 2

Factor $x^{2} - 8 x - 20$ 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 $- 20$ and whose sum is $- 8$ .

$- 10, 2$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 10) (x + 4)}{(x - 10) (x + 2)} \cdot \frac{x + 7}{x + 4}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $x + 4$ .

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Step 3.1.1

Factor $x + 4$ out of $(x - 10) (x + 4)$ .

$\frac{(x + 4) (x - 10)}{(x - 10) (x + 2)} \cdot \frac{x + 7}{x + 4}$

Step 3.1.2

Cancel the common factor.

$\frac{(x + 4) (x - 10)}{(x - 10) (x + 2)} \cdot \frac{x + 7}{x + 4}$

Step 3.1.3

Rewrite the expression.

$\frac{x - 10}{(x - 10) (x + 2)} \cdot (x + 7)$

Step 3.2

Cancel the common factor of $x - 10$ .

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Step 3.2.1

Cancel the common factor.

$\frac{x - 10}{(x - 10) (x + 2)} \cdot (x + 7)$

Step 3.2.2

Rewrite the expression.

$\frac{1}{x + 2} \cdot (x + 7)$

Step 3.3

Multiply $\frac{1}{x + 2}$ by $x + 7$ .

$\frac{x + 7}{x + 2}$