Basic Math Examples

$\frac{z^{2} - 8 z + 12}{z + 4} \cdot \frac{z + 4}{z^{2} + 3 z - 54}$

Step 1

Factor $z^{2} - 8 z + 12$ 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 $12$ and whose sum is $- 8$ .

$- 6, - 2$

Step 1.2

Write the factored form using these integers.

$\frac{(z - 6) (z - 2)}{z + 4} \cdot \frac{z + 4}{z^{2} + 3 z - 54}$

Step 2

Factor $z^{2} + 3 z - 54$ using the AC method.

Tap for more steps...

Step 2.1

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 $- 54$ and whose sum is $3$ .

$- 6, 9$

Step 2.2

Write the factored form using these integers.

$\frac{(z - 6) (z - 2)}{z + 4} \cdot \frac{z + 4}{(z - 6) (z + 9)}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $z - 6$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{(z - 6) (z - 2)}{z + 4} \cdot \frac{z + 4}{(z - 6) (z + 9)}$

Step 3.1.2

Rewrite the expression.

$\frac{z - 2}{z + 4} \cdot \frac{z + 4}{z + 9}$

Step 3.2

Cancel the common factor of $z + 4$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{z - 2}{z + 4} \cdot \frac{z + 4}{z + 9}$

Step 3.2.2

Rewrite the expression.

$(z - 2) \cdot \frac{1}{z + 9}$

Step 3.3

Multiply $z - 2$ by $\frac{1}{z + 9}$ .

$\frac{z - 2}{z + 9}$