Basic Math Examples

$\frac{(a - 3) a + 3}{a^{2} - 1} \div \frac{a + 2}{a - 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{(a - 3) a + 3}{a^{2} - 1} \cdot \frac{a - 3}{a + 2}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $a$ by $a$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

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 $b = 1$ .

$\frac{a^{2} - 3 a + 3}{(a + 1) (a - 1)} \cdot \frac{a - 3}{a + 2}$

Step 4

Multiply $\frac{a^{2} - 3 a + 3}{(a + 1) (a - 1)}$ by $\frac{a - 3}{a + 2}$ .

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