Algebra Examples

$\frac{5}{a^{2} + 3 a + 2} + \frac{5 a + 1}{a^{2} + 3 a + 2}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{5 + 5 a + 1}{a^{2} + 3 a + 2}$

Step 1.2

Add $5$ and $1$ .

$\frac{5 a + 6}{a^{2} + 3 a + 2}$

Step 2

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

$1, 2$

Step 2.2

Write the factored form using these integers.

$\frac{5 a + 6}{(a + 1) (a + 2)}$