Pre-Algebra Examples

$\frac{x - 2}{x^{2} + 3 x + 2}$

Step 1

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

$1, 2$

Step 1.2

Write the factored form using these integers.

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

Step 2

Split the fraction $\frac{x - 2}{(x + 1) (x + 2)}$ into two fractions.

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

Step 3

Move the negative in front of the fraction.

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