Simplify z-4*1/(z-4)

$z - 4 \cdot \frac{1}{z - 4}$

Step 1

Simplify each term.

Combine $- 4$ and $\frac{1}{z - 4}$ .

$z + \frac{- 4}{z - 4}$

Move the negative in front of the fraction.

$z - \frac{4}{z - 4}$

Step 2

To write $z$ as a fraction with a common denominator, multiply by $\frac{z - 4}{z - 4}$ .

$\frac{z (z - 4)}{z - 4} - \frac{4}{z - 4}$

Step 3

Combine the numerators over the common denominator.

$\frac{z (z - 4) - 4}{z - 4}$

Step 4

Simplify the numerator.

Apply the distributive property.

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

Multiply $z$ by $z$ .

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

Move $- 4$ to the left of $z$ .

$\frac{z^{2} - 4 z - 4}{z - 4}$