Finite Math Examples

$\frac{z^{2} - 5 z + 6}{z^{2} - 4}$

Step 1

Factor $z^{2} - 5 z + 6$ using the AC method.

Tap for more steps...

Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $- 5$ .

$- 3, - 2$

Step 1.2

Write the factored form using these integers.

$\frac{(z - 3) (z - 2)}{z^{2} - 4}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{(z - 3) (z - 2)}{z^{2} - 2^{2}}$

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 $a = z$ and $b = 2$ .

$\frac{(z - 3) (z - 2)}{(z + 2) (z - 2)}$

Step 3

Cancel the common factor of $z - 2$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{(z - 3) (z - 2)}{(z + 2) (z - 2)}$

Step 3.2

Rewrite the expression.

$\frac{z - 3}{z + 2}$