Simplify (8v-56)/(8v+48)*(v^2+9v+18)/(8v^2+24v)

$\frac{8 v - 56}{8 v + 48} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Simplify with factoring out.

Factor $8$ out of $8 v - 56$ .

Factor $8$ out of $8 v$ .

$\frac{8 (v) - 56}{8 v + 48} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $8$ out of $- 56$ .

$\frac{8 v + 8 \cdot - 7}{8 v + 48} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $8$ out of $8 v + 8 \cdot - 7$ .

$\frac{8 (v - 7)}{8 v + 48} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $8$ out of $8 v + 48$ .

Factor $8$ out of $8 v$ .

$\frac{8 (v - 7)}{8 (v) + 48} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $8$ out of $48$ .

$\frac{8 (v - 7)}{8 v + 8 \cdot 6} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $8$ out of $8 v + 8 \cdot 6$ .

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{v^{2} + 9 v + 18}{8 v^{2} + 24 v}$

Factor $v^{2} + 9 v + 18$ 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 $18$ and whose sum is $9$ .

$3, 6$

Write the factored form using these integers.

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 v^{2} + 24 v}$

Simplify terms.

Factor $8 v$ out of $8 v^{2} + 24 v$ .

Factor $8 v$ out of $8 v^{2}$ .

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 v (v) + 24 v}$

Factor $8 v$ out of $24 v$ .

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 v (v) + 8 v (3)}$

Factor $8 v$ out of $8 v (v) + 8 v (3)$ .

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 v (v + 3)}$

Cancel the common factor of $8$ .

Factor $8$ out of $8 v (v + 3)$ .

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 (v (v + 3))}$

Cancel the common factor.

$\frac{8 (v - 7)}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{8 (v (v + 3))}$

Rewrite the expression.

$\frac{v - 7}{8 (v + 6)} \cdot \frac{(v + 3) (v + 6)}{v (v + 3)}$

Cancel the common factor of $v + 6$ .

Factor $v + 6$ out of $8 (v + 6)$ .

$\frac{v - 7}{(v + 6) \cdot 8} \cdot \frac{(v + 3) (v + 6)}{v (v + 3)}$

Factor $v + 6$ out of $(v + 3) (v + 6)$ .

$\frac{v - 7}{(v + 6) \cdot 8} \cdot \frac{(v + 6) (v + 3)}{v (v + 3)}$

Cancel the common factor.

$\frac{v - 7}{(v + 6) \cdot 8} \cdot \frac{(v + 6) (v + 3)}{v (v + 3)}$

Rewrite the expression.

$\frac{v - 7}{8} \cdot \frac{v + 3}{v (v + 3)}$

Multiply $\frac{v - 7}{8}$ by $\frac{v + 3}{v (v + 3)}$ .

$\frac{(v - 7) (v + 3)}{8 (v (v + 3))}$

Cancel the common factor of $v + 3$ .

Cancel the common factor.

$\frac{(v - 7) (v + 3)}{8 (v (v + 3))}$

Rewrite the expression.

$\frac{v - 7}{8 (v)}$

$\frac{v - 7}{8 v}$

Simplify (8v-56)/(8v+48)*(v^2+9v+18)/(8v^2+24v)

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