Basic Math Examples

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

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

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

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

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

Step 1.2.2

Factor $a$ out of $- a$ .

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

Step 1.2.3

Factor $a$ out of $a \cdot a + a \cdot - 1$ .

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

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

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

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

Step 2.2

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 $b = 1$ .

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

Step 3

Cancel the common factor of $a - 1$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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