Simplify (2x^2+14x+12)/(4x+24)*(x+10)/(x^2+11x+10)

$\frac{2 x^{2} + 14 x + 12}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Simplify the numerator.

Factor $2$ out of $2 x^{2} + 14 x + 12$ .

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

$\frac{2 (x^{2}) + 14 x + 12}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $2$ out of $14 x$ .

$\frac{2 (x^{2}) + 2 (7 x) + 12}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $2$ out of $12$ .

$\frac{2 x^{2} + 2 (7 x) + 2 \cdot 6}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

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

$\frac{2 (x^{2} + 7 x) + 2 \cdot 6}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

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

$\frac{2 (x^{2} + 7 x + 6)}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

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.

$\frac{2 ((x + 1) (x + 6))}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

$\frac{2 (x + 1) (x + 6)}{4 x + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $4$ out of $4 x + 24$ .

Factor $4$ out of $4 x$ .

$\frac{2 (x + 1) (x + 6)}{4 (x) + 24} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $4$ out of $24$ .

$\frac{2 (x + 1) (x + 6)}{4 x + 4 \cdot 6} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $4$ out of $4 x + 4 \cdot 6$ .

$\frac{2 (x + 1) (x + 6)}{4 (x + 6)} \cdot \frac{x + 10}{x^{2} + 11 x + 10}$

Factor $x^{2} + 11 x + 10$ 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 $10$ and whose sum is $11$ .

$1, 10$

Write the factored form using these integers.

$\frac{2 (x + 1) (x + 6)}{4 (x + 6)} \cdot \frac{x + 10}{(x + 1) (x + 10)}$

Simplify terms.

Cancel the common factor of $x + 1$ .

Factor $x + 1$ out of $2 (x + 1) (x + 6)$ .

$\frac{(x + 1) (2 (x + 6))}{4 (x + 6)} \cdot \frac{x + 10}{(x + 1) (x + 10)}$

Cancel the common factor.

$\frac{(x + 1) (2 (x + 6))}{4 (x + 6)} \cdot \frac{x + 10}{(x + 1) (x + 10)}$

Rewrite the expression.

$\frac{2 (x + 6)}{4 (x + 6)} \cdot \frac{x + 10}{x + 10}$

Multiply $\frac{2 (x + 6)}{4 (x + 6)}$ by $\frac{x + 10}{x + 10}$ .

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 (x + 6) (x + 10)$ .

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

Cancel the common factors.

Factor $2$ out of $4 (x + 6) (x + 10)$ .

$\frac{2 ((x + 6) (x + 10))}{2 (2 (x + 6) (x + 10))}$

Cancel the common factor.

$\frac{2 ((x + 6) (x + 10))}{2 (2 (x + 6) (x + 10))}$

Rewrite the expression.

$\frac{(x + 6) (x + 10)}{2 (x + 6) (x + 10)}$

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{(x + 6) (x + 10)}{2 (x + 6) (x + 10)}$

Rewrite the expression.

$\frac{x + 10}{2 (x + 10)}$

Cancel the common factor of $x + 10$ .

Cancel the common factor.

$\frac{x + 10}{2 (x + 10)}$

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Simplify (2x^2+14x+12)/(4x+24)*(x+10)/(x^2+11x+10)

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