Simplify ((x^2+10x+16)/(x^2+6x+8))÷(1/(x+4))

$\frac{x^{2} + 10 x + 16}{x^{2} + 6 x + 8} \div \frac{1}{x + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} + 10 x + 16}{x^{2} + 6 x + 8} (x + 4)$

Step 2

Factor $x^{2} + 10 x + 16$ 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 $16$ and whose sum is $10$ .

$2, 8$

Write the factored form using these integers.

$\frac{(x + 2) (x + 8)}{x^{2} + 6 x + 8} (x + 4)$

Step 3

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.

$\frac{(x + 2) (x + 8)}{(x + 2) (x + 4)} (x + 4)$

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $(x + 2) (x + 4)$ .

$\frac{(x + 2) (x + 8)}{(x + 4) (x + 2)} (x + 4)$

Cancel the common factor.

$\frac{(x + 2) (x + 8)}{(x + 4) (x + 2)} (x + 4)$

Rewrite the expression.

$\frac{(x + 2) (x + 8)}{x + 2}$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x + 2) (x + 8)}{x + 2}$

Divide $x + 8$ by $1$ .

$x + 8$

Simplify ((x^2+10x+16)/(x^2+6x+8))÷(1/(x+4))

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