Algebra Examples

$(- q^{3} - 3 q) \div 9 q^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{- q^{3} - 3 q}{9 q^{3}}$

Step 2

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

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Step 2.1

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

$\frac{q (- q^{2}) - 3 q}{9 q^{3}}$

Step 2.2

Factor $q$ out of $- 3 q$ .

$\frac{q (- q^{2}) + q \cdot - 3}{9 q^{3}}$

Step 2.3

Factor $q$ out of $q (- q^{2}) + q \cdot - 3$ .

$\frac{q (- q^{2} - 3)}{9 q^{3}}$

$\frac{q (- q^{2} - 3)}{9 q^{3}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $q$ out of $9 q^{3}$ .

$\frac{q (- q^{2} - 3)}{q (9 q^{2})}$

Step 3.2

Cancel the common factor.

$\frac{q (- q^{2} - 3)}{q (9 q^{2})}$

Step 3.3

Rewrite the expression.

$\frac{- q^{2} - 3}{9 q^{2}}$

$\frac{- q^{2} - 3}{9 q^{2}}$

Step 4

Factor $- 1$ out of $- q^{2}$ .

$\frac{- (q^{2}) - 3}{9 q^{2}}$

Step 5

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (q^{2}) - 1 (3)}{9 q^{2}}$

Step 6

Factor $- 1$ out of $- (q^{2}) - 1 (3)$ .

$\frac{- (q^{2} + 3)}{9 q^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Rewrite $- (q^{2} + 3)$ as $- 1 (q^{2} + 3)$ .

$\frac{- 1 (q^{2} + 3)}{9 q^{2}}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{q^{2} + 3}{9 q^{2}}$

$- \frac{q^{2} + 3}{9 q^{2}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$