Algebra Examples

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

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 $5 p^{3} - 35 p^{2}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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 $9 p - 36$ .

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Step 3.1

Factor $9$ out of $9 p$ .

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

Step 3.2

Factor $9$ out of $- 36$ .

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

Step 3.3

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 $5$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Multiply $p - 7$ by $1$ .

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