Pre-Algebra Examples

$\frac{2 x + 5}{x^{2} + 7 x + 12}$

Step 1

Factor $x^{2} + 7 x + 12$ 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 $12$ and whose sum is $7$ .

$3, 4$

Step 1.2

Write the factored form using these integers.

$\frac{2 x + 5}{(x + 3) (x + 4)}$

Step 2

Split the fraction $\frac{2 x + 5}{(x + 3) (x + 4)}$ into two fractions.

$\frac{2 x}{(x + 3) (x + 4)} + \frac{5}{(x + 3) (x + 4)}$