Pre-Algebra Examples

$(- a^{3} b^{2} + a^{2} b^{3} - a b^{3}) \div (- a^{2} b^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- a^{3} b^{2} + a^{2} b^{3} - a b^{3}}{- a^{2} b^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $a b^{2}$ out of $- a^{3} b^{2} + a^{2} b^{3} - a b^{3}$ .

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Step 2.1.1

Factor $a b^{2}$ out of $- a^{3} b^{2}$ .

$\frac{a b^{2} (- a^{2}) + a^{2} b^{3} - a b^{3}}{- a^{2} b^{2}}$

Step 2.1.2

Factor $a b^{2}$ out of $a^{2} b^{3}$ .

$\frac{a b^{2} (- a^{2}) + a b^{2} (a b) - a b^{3}}{- a^{2} b^{2}}$

Step 2.1.3

Factor $a b^{2}$ out of $- a b^{3}$ .

$\frac{a b^{2} (- a^{2}) + a b^{2} (a b) + a b^{2} (- 1 b)}{- a^{2} b^{2}}$

Step 2.1.4

Factor $a b^{2}$ out of $a b^{2} (- a^{2}) + a b^{2} (a b)$ .

$\frac{a b^{2} (- a^{2} + a b) + a b^{2} (- 1 b)}{- a^{2} b^{2}}$

Step 2.1.5

Factor $a b^{2}$ out of $a b^{2} (- a^{2} + a b) + a b^{2} (- 1 b)$ .

$\frac{a b^{2} (- a^{2} + a b - 1 b)}{- a^{2} b^{2}}$

Step 2.2

Rewrite $- 1 b$ as $- b$ .

$\frac{a b^{2} (- a^{2} + a b - b)}{- a^{2} b^{2}}$

Step 3

Cancel the common factor of $a$ and $a^{2}$ .

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Step 3.1

Factor $a$ out of $a b^{2} (- a^{2} + a b - b)$ .

$\frac{a (b^{2} (- a^{2} + a b - b))}{- a^{2} b^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $- a^{2} b^{2}$ .

$\frac{a (b^{2} (- a^{2} + a b - b))}{a (- a b^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{a (b^{2} (- a^{2} + a b - b))}{a (- a b^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{b^{2} (- a^{2} + a b - b)}{- a b^{2}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{b^{2} (- a^{2} + a b - b)}{- a b^{2}}$

Step 4.2

Rewrite the expression.

$\frac{- a^{2} + a b - b}{- a}$

Step 5

Move the negative in front of the fraction.

$- \frac{- a^{2} + a b - b}{a}$

Step 6

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

$- \frac{- (a^{2}) + a b - b}{a}$

Step 7

Factor $- 1$ out of $a b$ .

$- \frac{- (a^{2}) - (- a b) - b}{a}$

Step 8

Factor $- 1$ out of $- (a^{2}) - (- a b)$ .

$- \frac{- (a^{2} - a b) - b}{a}$

Step 9

Factor $- 1$ out of $- b$ .

$- \frac{- (a^{2} - a b) - (b)}{a}$

Step 10

Factor $- 1$ out of $- (a^{2} - a b) - (b)$ .

$- \frac{- (a^{2} - a b + b)}{a}$

Step 11

Rewrite $- (a^{2} - a b + b)$ as $- 1 (a^{2} - a b + b)$ .

$- \frac{- 1 (a^{2} - a b + b)}{a}$

Step 12

Move the negative in front of the fraction.

$- - \frac{a^{2} - a b + b}{a}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \frac{a^{2} - a b + b}{a}$

Step 14

Multiply $\frac{a^{2} - a b + b}{a}$ by $1$ .

$\frac{a^{2} - a b + b}{a}$

Step 15

Split the fraction $\frac{a^{2} - a b + b}{a}$ into two fractions.

$\frac{a^{2} - a b}{a} + \frac{b}{a}$

Step 16

Split the fraction $\frac{a^{2} - a b}{a}$ into two fractions.

$\frac{a^{2}}{a} + \frac{- a b}{a} + \frac{b}{a}$

Step 17

Cancel the common factor of $a^{2}$ and $a$ .

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Step 17.1

Factor $a$ out of $a^{2}$ .

$\frac{a \cdot a}{a} + \frac{- a b}{a} + \frac{b}{a}$

Step 17.2

Cancel the common factors.

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Step 17.2.1

Raise $a$ to the power of $1$ .

$\frac{a \cdot a}{a^{1}} + \frac{- a b}{a} + \frac{b}{a}$

Step 17.2.2

Factor $a$ out of $a^{1}$ .

$\frac{a \cdot a}{a \cdot 1} + \frac{- a b}{a} + \frac{b}{a}$

Step 17.2.3

Cancel the common factor.

$\frac{a \cdot a}{a \cdot 1} + \frac{- a b}{a} + \frac{b}{a}$

Step 17.2.4

Rewrite the expression.

$\frac{a}{1} + \frac{- a b}{a} + \frac{b}{a}$

Step 17.2.5

Divide $a$ by $1$ .

$a + \frac{- a b}{a} + \frac{b}{a}$

Step 18

Cancel the common factor of $a$ .

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Step 18.1

Cancel the common factor.

$a + \frac{- a b}{a} + \frac{b}{a}$

Step 18.2

Divide $- 1 b$ by $1$ .

$a - 1 b + \frac{b}{a}$

Step 19

Rewrite $- 1 b$ as $- b$ .

$a - b + \frac{b}{a}$