Simplify (x+3)/4*(x+2)/(x^2+4x+3)

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

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.

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

Simplify terms.

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of $(x + 1) (x + 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{4}$ by $\frac{x + 2}{x + 1}$ .

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

Simplify (x+3)/4*(x+2)/(x^2+4x+3)

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