Simplify (8x^3)/(2x+12)*(x^2+7x+6)/(4x^5)

$\frac{8 x^{3}}{2 x + 12} \cdot \frac{x^{2} + 7 x + 6}{4 x^{5}}$

Step 1

Factor $2$ out of $2 x + 12$ .

Factor $2$ out of $2 x$ .

$\frac{8 x^{3}}{2 (x) + 12} \cdot \frac{x^{2} + 7 x + 6}{4 x^{5}}$

Factor $2$ out of $12$ .

$\frac{8 x^{3}}{2 x + 2 \cdot 6} \cdot \frac{x^{2} + 7 x + 6}{4 x^{5}}$

Factor $2$ out of $2 x + 2 \cdot 6$ .

$\frac{8 x^{3}}{2 (x + 6)} \cdot \frac{x^{2} + 7 x + 6}{4 x^{5}}$

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.

$\frac{8 x^{3}}{2 (x + 6)} \cdot \frac{(x + 1) (x + 6)}{4 x^{5}}$

Step 3

Simplify terms.

Combine.

$\frac{8 x^{3} ((x + 1) (x + 6))}{2 (x + 6) (4 x^{5})}$

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 x^{3} ((x + 1) (x + 6))$ .

$\frac{2 (4 x^{3} ((x + 1) (x + 6)))}{2 (x + 6) (4 x^{5})}$

Cancel the common factors.

Factor $2$ out of $2 (x + 6) (4 x^{5})$ .

$\frac{2 (4 x^{3} ((x + 1) (x + 6)))}{2 ((x + 6) (4 x^{5}))}$

Cancel the common factor.

$\frac{2 (4 x^{3} ((x + 1) (x + 6)))}{2 ((x + 6) (4 x^{5}))}$

Rewrite the expression.

$\frac{4 x^{3} ((x + 1) (x + 6))}{(x + 6) (4 x^{5})}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{3} ((x + 1) (x + 6))}{(x + 6) (4 x^{5})}$

Rewrite the expression.

$\frac{x^{3} ((x + 1) (x + 6))}{(x + 6) (x^{5})}$

Step 4

Cancel the common factors.

Factor $x^{3}$ out of $(x + 6) (x^{5})$ .

$\frac{x^{3} ((x + 1) (x + 6))}{x^{3} ((x + 6) (x^{2}))}$

Cancel the common factor.

$\frac{x^{3} ((x + 1) (x + 6))}{x^{3} ((x + 6) (x^{2}))}$

Rewrite the expression.

$\frac{(x + 1) (x + 6)}{(x + 6) (x^{2})}$

Step 5

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$\frac{(x + 1) (x + 6)}{(x + 6) x^{2}}$

Rewrite the expression.

$\frac{x + 1}{x^{2}}$

Simplify (8x^3)/(2x+12)*(x^2+7x+6)/(4x^5)

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