Finite Math Examples

$\frac{x^{2} - 6 x - 7}{x^{2} - 2 x - 3}$

Step 1

Factor $x^{2} - 6 x - 7$ 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 $- 7$ and whose sum is $- 6$ .

$- 7, 1$

Step 1.2

Write the factored form using these integers.

$\frac{(x - 7) (x + 1)}{x^{2} - 2 x - 3}$

Step 2

Factor $x^{2} - 2 x - 3$ 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 $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 2.2

Write the factored form using these integers.

$\frac{(x - 7) (x + 1)}{(x - 3) (x + 1)}$

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(x - 7) (x + 1)}{(x - 3) (x + 1)}$

Step 3.2

Rewrite the expression.

$\frac{x - 7}{x - 3}$