Algebra Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $a$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = 1$ .

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

Step 4

Cancel the common factor of $a - 1$ .

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Step 4.1

Factor $a - 1$ out of $(a + 1) (a - 1)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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