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

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

Factor $8$ out of $8 x + 8$ .

Factor $8$ out of $8 x$ .

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

Factor $8$ out of $8$ .

$\frac{4 x}{8 (x) + 8 (1)} \cdot \frac{x^{2} + 8 x + 7}{8 x^{3}}$

Factor $8$ out of $8 (x) + 8 (1)$ .

$\frac{4 x}{8 (x + 1)} \cdot \frac{x^{2} + 8 x + 7}{8 x^{3}}$

Factor $x^{2} + 8 x + 7$ 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 $7$ and whose sum is $8$ .

$1, 7$

Write the factored form using these integers.

$\frac{4 x}{8 (x + 1)} \cdot \frac{(x + 1) (x + 7)}{8 x^{3}}$

Simplify terms.

Combine.

$\frac{4 x ((x + 1) (x + 7))}{8 (x + 1) (8 x^{3})}$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 x ((x + 1) (x + 7))$ .

$\frac{4 (x ((x + 1) (x + 7)))}{8 (x + 1) (8 x^{3})}$

Cancel the common factors.

Factor $4$ out of $8 (x + 1) (8 x^{3})$ .

$\frac{4 (x ((x + 1) (x + 7)))}{4 (2 (x + 1) (8 x^{3}))}$

Cancel the common factor.

$\frac{4 (x ((x + 1) (x + 7)))}{4 (2 (x + 1) (8 x^{3}))}$

Rewrite the expression.

$\frac{x ((x + 1) (x + 7))}{2 (x + 1) (8 x^{3})}$

Cancel the common factors.

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

$\frac{x ((x + 1) (x + 7))}{x (2 (x + 1) (8 x^{2}))}$

Cancel the common factor.

$\frac{x ((x + 1) (x + 7))}{x (2 (x + 1) (8 x^{2}))}$

Rewrite the expression.

$\frac{(x + 1) (x + 7)}{2 (x + 1) (8 x^{2})}$

Cancel the common factor of $x + 1$ .

Cancel the common factor.

$\frac{(x + 1) (x + 7)}{2 (x + 1) (8 x^{2})}$

Rewrite the expression.

$\frac{x + 7}{2 (8 x^{2})}$

Multiply $2$ by $8$ .

$\frac{x + 7}{16 x^{2}}$

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

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