Simplify 1/(2x+6)+(x+1)/(x^2+4x+3)

$\frac{1}{2 x + 6} + \frac{x + 1}{x^{2} + 4 x + 3}$

Simplify each term.

Factor $2$ out of $2 x + 6$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2 (x) + 6} + \frac{x + 1}{x^{2} + 4 x + 3}$

Factor $2$ out of $6$ .

$\frac{1}{2 x + 2 \cdot 3} + \frac{x + 1}{x^{2} + 4 x + 3}$

Factor $2$ out of $2 x + 2 \cdot 3$ .

$\frac{1}{2 (x + 3)} + \frac{x + 1}{x^{2} + 4 x + 3}$

Factor $x^{2} + 4 x + 3$ using the AC method.

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 $3$ and whose sum is $4$ .

$1, 3$

Write the factored form using these integers.

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

To write $\frac{1}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $2 (x + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x + 3}$ by $\frac{2}{2}$ .

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

Reorder the factors of $(x + 3) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Add $1$ and $2$ .

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

Simplify 1/(2x+6)+(x+1)/(x^2+4x+3)

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