Pre-Algebra Examples

$\frac{z^{2}}{z - 2} - \frac{11 z - 18}{z - 2}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{z^{2} - (11 z - 18)}{z - 2}$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$\frac{z^{2} - (11 z) - - 18}{z - 2}$

Step 1.2.2

Multiply $11$ by $- 1$ .

$\frac{z^{2} - 11 z - - 18}{z - 2}$

Step 1.2.3

Multiply $- 1$ by $- 18$ .

$\frac{z^{2} - 11 z + 18}{z - 2}$

Step 2

Factor $z^{2} - 11 z + 18$ 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 $18$ and whose sum is $- 11$ .

$- 9, - 2$

Step 2.2

Write the factored form using these integers.

$\frac{(z - 9) (z - 2)}{z - 2}$

Step 3

Cancel the common factor of $z - 2$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{(z - 9) (z - 2)}{z - 2}$

Step 3.2

Divide $z - 9$ by $1$ .

$z - 9$