Pre-Algebra Examples

$\frac{- a^{3} b^{2} + a^{2} b^{3} - 6 a b^{2}}{- 27 a^{2} b^{3}}$

Step 1

Factor $a b^{2}$ out of $- a^{3} b^{2} + a^{2} b^{3} - 6 a b^{2}$ .

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Step 1.1

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

$\frac{a b^{2} (- a^{2}) + a^{2} b^{3} - 6 a b^{2}}{- 27 a^{2} b^{3}}$

Step 1.2

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

$\frac{a b^{2} (- a^{2}) + a b^{2} (a b) - 6 a b^{2}}{- 27 a^{2} b^{3}}$

Step 1.3

Factor $a b^{2}$ out of $- 6 a b^{2}$ .

$\frac{a b^{2} (- a^{2}) + a b^{2} (a b) + a b^{2} (- 6)}{- 27 a^{2} b^{3}}$

Step 1.4

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

$\frac{a b^{2} (- a^{2} + a b) + a b^{2} (- 6)}{- 27 a^{2} b^{3}}$

Step 1.5

Factor $a b^{2}$ out of $a b^{2} (- a^{2} + a b) + a b^{2} (- 6)$ .

$\frac{a b^{2} (- a^{2} + a b - 6)}{- 27 a^{2} b^{3}}$

Step 2

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

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Step 2.1

Factor $a$ out of $a b^{2} (- a^{2} + a b - 6)$ .

$\frac{a (b^{2} (- a^{2} + a b - 6))}{- 27 a^{2} b^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a$ out of $- 27 a^{2} b^{3}$ .

$\frac{a (b^{2} (- a^{2} + a b - 6))}{a (- 27 a b^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{a (b^{2} (- a^{2} + a b - 6))}{a (- 27 a b^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{b^{2} (- a^{2} + a b - 6)}{- 27 a b^{3}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $b^{2}$ out of $- 27 a b^{3}$ .

$\frac{b^{2} (- a^{2} + a b - 6)}{b^{2} (- 27 a b)}$

Step 3.2

Cancel the common factor.

$\frac{b^{2} (- a^{2} + a b - 6)}{b^{2} (- 27 a b)}$

Step 3.3

Rewrite the expression.

$\frac{- a^{2} + a b - 6}{- 27 a b}$

Step 4

Move the negative in front of the fraction.

$- \frac{- a^{2} + a b - 6}{27 a b}$

Step 5

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

$- \frac{- (a^{2}) + a b - 6}{27 a b}$

Step 6

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

$- \frac{- (a^{2}) - (- a b) - 6}{27 a b}$

Step 7

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

$- \frac{- (a^{2} - a b) - 6}{27 a b}$

Step 8

Rewrite $- 6$ as $- 1 (6)$ .

$- \frac{- (a^{2} - a b) - 1 (6)}{27 a b}$

Step 9

Factor $- 1$ out of $- (a^{2} - a b) - 1 (6)$ .

$- \frac{- (a^{2} - a b + 6)}{27 a b}$

Step 10

Rewrite $- (a^{2} - a b + 6)$ as $- 1 (a^{2} - a b + 6)$ .

$- \frac{- 1 (a^{2} - a b + 6)}{27 a b}$

Step 11

Move the negative in front of the fraction.

$- - \frac{a^{2} - a b + 6}{27 a b}$

Step 12

Multiply $- 1$ by $- 1$ .

$1 \frac{a^{2} - a b + 6}{27 a b}$

Step 13

Multiply $\frac{a^{2} - a b + 6}{27 a b}$ by $1$ .

$\frac{a^{2} - a b + 6}{27 a b}$

Step 14

Split the fraction $\frac{a^{2} - a b + 6}{27 a b}$ into two fractions.

$\frac{a^{2} - a b}{27 a b} + \frac{6}{27 a b}$

Step 15

Split the fraction $\frac{a^{2} - a b}{27 a b}$ into two fractions.

$\frac{a^{2}}{27 a b} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 16

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

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Step 16.1

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

$\frac{a \cdot a}{27 a b} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $a$ out of $27 a b$ .

$\frac{a \cdot a}{a (27 b)} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 16.2.2

Cancel the common factor.

$\frac{a \cdot a}{a (27 b)} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 16.2.3

Rewrite the expression.

$\frac{a}{27 b} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 17

Cancel the common factor of $a$ .

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Step 17.1

Cancel the common factor.

$\frac{a}{27 b} + \frac{- a b}{27 a b} + \frac{6}{27 a b}$

Step 17.2

Rewrite the expression.

$\frac{a}{27 b} + \frac{- 1 b}{27 b} + \frac{6}{27 a b}$

Step 18

Cancel the common factor of $b$ .

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Step 18.1

Cancel the common factor.

$\frac{a}{27 b} + \frac{- 1 b}{27 b} + \frac{6}{27 a b}$

Step 18.2

Rewrite the expression.

$\frac{a}{27 b} + \frac{- 1}{27} + \frac{6}{27 a b}$

Step 19

Move the negative in front of the fraction.

$\frac{a}{27 b} - \frac{1}{27} + \frac{6}{27 a b}$

Step 20

Cancel the common factor of $6$ and $27$ .

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Step 20.1

Factor $3$ out of $6$ .

$\frac{a}{27 b} - \frac{1}{27} + \frac{3 (2)}{27 a b}$

Step 20.2

Cancel the common factors.

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Step 20.2.1

Factor $3$ out of $27 a b$ .

$\frac{a}{27 b} - \frac{1}{27} + \frac{3 (2)}{3 (9 a b)}$

Step 20.2.2

Cancel the common factor.

$\frac{a}{27 b} - \frac{1}{27} + \frac{3 \cdot 2}{3 (9 a b)}$

Step 20.2.3

Rewrite the expression.

$\frac{a}{27 b} - \frac{1}{27} + \frac{2}{9 a b}$