Pre-Algebra Examples

$\frac{a - a b}{a^{2}} \div \frac{a - 1}{a^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a - a b}{a^{2}} \cdot \frac{a^{3}}{a - 1}$

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

$(a - a b) \frac{a}{a - 1}$

Step 2.2

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

$\frac{(a - a b) a}{a - 1}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

$\frac{(a \cdot 1 - a b) a}{a - 1}$

Step 3.1.3

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

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

Step 3.1.4

Factor $a$ out of $a \cdot 1 + a (- 1 b)$ .

$\frac{a (1 - 1 b) a}{a - 1}$

Step 3.2

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

$\frac{a (1 - b) a}{a - 1}$

Step 3.3

Combine exponents.

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Step 3.3.1

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

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

Step 3.3.2

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

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

Step 3.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.3.4

Add $1$ and $1$ .

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