Algebra Examples

$\frac{45 p^{5} q^{4} - 60 p^{3} q^{2} - 15 p^{2} q^{3}}{15 p^{2} q^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $15 p^{2} q^{2}$ out of $45 p^{5} q^{4} - 60 p^{3} q^{2} - 15 p^{2} q^{3}$ .

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Step 1.1.1

Factor $15 p^{2} q^{2}$ out of $45 p^{5} q^{4}$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2}) - 60 p^{3} q^{2} - 15 p^{2} q^{3}}{15 p^{2} q^{3}}$

Step 1.1.2

Factor $15 p^{2} q^{2}$ out of $- 60 p^{3} q^{2}$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2}) + 15 p^{2} q^{2} (- 4 p) - 15 p^{2} q^{3}}{15 p^{2} q^{3}}$

Step 1.1.3

Factor $15 p^{2} q^{2}$ out of $- 15 p^{2} q^{3}$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2}) + 15 p^{2} q^{2} (- 4 p) + 15 p^{2} q^{2} (- 1 q)}{15 p^{2} q^{3}}$

Step 1.1.4

Factor $15 p^{2} q^{2}$ out of $15 p^{2} q^{2} (3 p^{3} q^{2}) + 15 p^{2} q^{2} (- 4 p)$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2} - 4 p) + 15 p^{2} q^{2} (- 1 q)}{15 p^{2} q^{3}}$

Step 1.1.5

Factor $15 p^{2} q^{2}$ out of $15 p^{2} q^{2} (3 p^{3} q^{2} - 4 p) + 15 p^{2} q^{2} (- 1 q)$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2} - 4 p - 1 q)}{15 p^{2} q^{3}}$

Step 1.2

Rewrite $- 1 q$ as $- q$ .

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2} - 4 p - q)}{15 p^{2} q^{3}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $15$ .

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Step 2.1.1

Cancel the common factor.

$\frac{15 p^{2} q^{2} (3 p^{3} q^{2} - 4 p - q)}{15 p^{2} q^{3}}$

Step 2.1.2

Rewrite the expression.

$\frac{p^{2} q^{2} (3 p^{3} q^{2} - 4 p - q)}{p^{2} q^{3}}$

Step 2.2

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

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Step 2.2.1

Cancel the common factor.

$\frac{p^{2} q^{2} (3 p^{3} q^{2} - 4 p - q)}{p^{2} q^{3}}$

Step 2.2.2

Rewrite the expression.

$\frac{q^{2} (3 p^{3} q^{2} - 4 p - q)}{q^{3}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $q^{2}$ out of $q^{3}$ .

$\frac{q^{2} (3 p^{3} q^{2} - 4 p - q)}{q^{2} q}$

Step 3.2

Cancel the common factor.

$\frac{q^{2} (3 p^{3} q^{2} - 4 p - q)}{q^{2} q}$

Step 3.3

Rewrite the expression.

$\frac{3 p^{3} q^{2} - 4 p - q}{q}$