Simplify (2x+12)/(2x^2+14x+12)

$\frac{2 x + 12}{2 x^{2} + 14 x + 12}$

Step 1

Cancel the common factor of $2 x + 12$ and $2 x^{2} + 14 x + 12$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 12}{2 x^{2} + 14 x + 12}$

Factor $2$ out of $12$ .

$\frac{2 (x) + 2 \cdot 6}{2 x^{2} + 14 x + 12}$

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

$\frac{2 (x + 6)}{2 x^{2} + 14 x + 12}$

Cancel the common factors.

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x + 6)}{2 (x^{2}) + 14 x + 12}$

Factor $2$ out of $14 x$ .

$\frac{2 (x + 6)}{2 (x^{2}) + 2 (7 x) + 12}$

Factor $2$ out of $2 (x^{2}) + 2 (7 x)$ .

$\frac{2 (x + 6)}{2 (x^{2} + 7 x) + 12}$

Factor $2$ out of $12$ .

$\frac{2 (x + 6)}{2 (x^{2} + 7 x) + 2 \cdot 6}$

Factor $2$ out of $2 (x^{2} + 7 x) + 2 \cdot 6$ .

$\frac{2 (x + 6)}{2 (x^{2} + 7 x + 6)}$

Cancel the common factor.

$\frac{2 (x + 6)}{2 (x^{2} + 7 x + 6)}$

Rewrite the expression.

$\frac{x + 6}{x^{2} + 7 x + 6}$

Step 2

Factor $x^{2} + 7 x + 6$ 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 $6$ and whose sum is $7$ .

$1, 6$

Write the factored form using these integers.

$\frac{x + 6}{(x + 1) (x + 6)}$

Step 3

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{x + 6}{(x + 1) (x + 6)}$

Rewrite the expression.

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

Simplify (2x+12)/(2x^2+14x+12)

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