Simplify ((p-7)/8)÷((p+5)/(8p+8))

$\frac{p - 7}{8} \div \frac{p + 5}{8 p + 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{p - 7}{8} \cdot \frac{8 p + 8}{p + 5}$

Step 2

Factor $8$ out of $8 p + 8$ .

Factor $8$ out of $8 p$ .

$\frac{p - 7}{8} \cdot \frac{8 (p) + 8}{p + 5}$

Factor $8$ out of $8$ .

$\frac{p - 7}{8} \cdot \frac{8 (p) + 8 (1)}{p + 5}$

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

$\frac{p - 7}{8} \cdot \frac{8 (p + 1)}{p + 5}$

Step 3

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{p - 7}{8} \cdot \frac{8 (p + 1)}{p + 5}$

Rewrite the expression.

$(p - 7) \frac{p + 1}{p + 5}$

Step 4

Multiply $p - 7$ by $\frac{p + 1}{p + 5}$ .

$\frac{(p - 7) (p + 1)}{p + 5}$