Simplify (1/(5p^2))÷((9p-36)/(5p^3-35p^2))

$\frac{1}{5 p^{2}} \div \frac{9 p - 36}{5 p^{3} - 35 p^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{3} - 35 p^{2}}{9 p - 36}$

Step 2

Factor $5 p^{2}$ out of $5 p^{3} - 35 p^{2}$ .

Factor $5 p^{2}$ out of $5 p^{3}$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p) - 35 p^{2}}{9 p - 36}$

Factor $5 p^{2}$ out of $- 35 p^{2}$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p) + 5 p^{2} (- 7)}{9 p - 36}$

Factor $5 p^{2}$ out of $5 p^{2} (p) + 5 p^{2} (- 7)$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p - 7)}{9 p - 36}$

Step 3

Factor $9$ out of $9 p - 36$ .

Factor $9$ out of $9 p$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p - 7)}{9 (p) - 36}$

Factor $9$ out of $- 36$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p - 7)}{9 p + 9 \cdot - 4}$

Factor $9$ out of $9 p + 9 \cdot - 4$ .

$\frac{1}{5 p^{2}} \cdot \frac{5 p^{2} (p - 7)}{9 (p - 4)}$

Step 4

Combine.

$\frac{1 (5 p^{2} (p - 7))}{5 p^{2} (9 (p - 4))}$

Step 5

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{1 (5 p^{2} (p - 7))}{5 p^{2} (9 (p - 4))}$

Rewrite the expression.

$\frac{1 (p^{2} (p - 7))}{p^{2} (9 (p - 4))}$

Step 6

Cancel the common factor of $p^{2}$ .

Cancel the common factor.

$\frac{1 (p^{2} (p - 7))}{p^{2} (9 (p - 4))}$

Rewrite the expression.

$\frac{1 (p - 7)}{9 (p - 4)}$

Step 7

Multiply $p - 7$ by $1$ .

$\frac{p - 7}{9 (p - 4)}$