Simplify (3x+9)/(4x^4)*(2x^2+4x)/(x^2+10x+21)

$\frac{3 x + 9}{4 x^{4}} \cdot \frac{2 x^{2} + 4 x}{x^{2} + 10 x + 21}$

Step 1

Simplify with factoring out.

Factor $3$ out of $3 x + 9$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 9}{4 x^{4}} \cdot \frac{2 x^{2} + 4 x}{x^{2} + 10 x + 21}$

Factor $3$ out of $9$ .

$\frac{3 x + 3 \cdot 3}{4 x^{4}} \cdot \frac{2 x^{2} + 4 x}{x^{2} + 10 x + 21}$

Factor $3$ out of $3 x + 3 \cdot 3$ .

$\frac{3 (x + 3)}{4 x^{4}} \cdot \frac{2 x^{2} + 4 x}{x^{2} + 10 x + 21}$

Factor $2 x$ out of $2 x^{2} + 4 x$ .

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

$\frac{3 (x + 3)}{4 x^{4}} \cdot \frac{2 x (x) + 4 x}{x^{2} + 10 x + 21}$

Factor $2 x$ out of $4 x$ .

$\frac{3 (x + 3)}{4 x^{4}} \cdot \frac{2 x (x) + 2 x (2)}{x^{2} + 10 x + 21}$

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

$\frac{3 (x + 3)}{4 x^{4}} \cdot \frac{2 x (x + 2)}{x^{2} + 10 x + 21}$

Step 2

Factor $x^{2} + 10 x + 21$ 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 $21$ and whose sum is $10$ .

$3, 7$

Write the factored form using these integers.

$\frac{3 (x + 3)}{4 x^{4}} \cdot \frac{2 x (x + 2)}{(x + 3) (x + 7)}$

Step 3

Simplify terms.

Combine.

$\frac{3 (x + 3) (2 x (x + 2))}{4 x^{4} ((x + 3) (x + 7))}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{3 (x + 3) (2 x (x + 2))}{4 x^{4} ((x + 3) (x + 7))}$

Rewrite the expression.

$\frac{3 (2 x (x + 2))}{4 x^{4} (x + 7)}$

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

Factor $2$ out of $3 (2 x (x + 2))$ .

$\frac{2 (3 (x (x + 2)))}{4 x^{4} (x + 7)}$

Cancel the common factors.

Factor $2$ out of $4 x^{4} (x + 7)$ .

$\frac{2 (3 (x (x + 2)))}{2 (2 x^{4} (x + 7))}$

Cancel the common factor.

$\frac{2 (3 (x (x + 2)))}{2 (2 x^{4} (x + 7))}$

Rewrite the expression.

$\frac{3 (x (x + 2))}{2 x^{4} (x + 7)}$

Cancel the common factor of $x$ and $x^{4}$ .

Factor $x$ out of $3 (x (x + 2))$ .

$\frac{x (3 (x + 2))}{2 x^{4} (x + 7)}$

Cancel the common factors.

Factor $x$ out of $2 x^{4} (x + 7)$ .

$\frac{x (3 (x + 2))}{x (2 x^{3} (x + 7))}$

Cancel the common factor.

$\frac{x (3 (x + 2))}{x (2 x^{3} (x + 7))}$

Rewrite the expression.

$\frac{3 (x + 2)}{2 x^{3} (x + 7)}$

Simplify (3x+9)/(4x^4)*(2x^2+4x)/(x^2+10x+21)

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