Pre-Algebra Examples

$(x - 5) \div (x^{2} - 3 x - 10)$

Step 1

Rewrite the division as a fraction.

$\frac{x - 5}{x^{2} - 3 x - 10}$

Step 2

Factor $x^{2} - 3 x - 10$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Step 2.2

Write the factored form using these integers.

$\frac{x - 5}{(x - 5) (x + 2)}$

Step 3

Cancel the common factor of $x - 5$ .

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Step 3.1

Cancel the common factor.

$\frac{x - 5}{(x - 5) (x + 2)}$

Step 3.2

Rewrite the expression.

$\frac{1}{x + 2}$