Algebra Examples

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

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.

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

Step 2

Combine into one fraction.

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Step 2.1

Reorder the factors of $(x + 2) (x + 1)$ .

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

Step 2.2

Combine the numerators over the common denominator.

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