Find the Product (x^2+6x+8)/(x^2+4x+3)*(x+3)/(x+2)

$\frac{x^{2} + 6 x + 8}{x^{2} + 4 x + 3} \cdot \frac{x + 3}{x + 2}$

Step 1

Factor $x^{2} + 6 x + 8$ 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 $8$ and whose sum is $6$ .

$2, 4$

Write the factored form using these integers.

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

Step 2

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.

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Find the Product (x^2+6x+8)/(x^2+4x+3)*(x+3)/(x+2)

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